Metrics for Data.Histogram.Bin.BinF:$cfromIndex from histogram-fill-0.8.4.1

analyze0.0ms (0%)

Memory

0.9MiB live, 0.9MiB allocated

Algorithm

1×

Search

Probability	Valid	Unknown	Precondition	Infinite	Domain	Can't	Iter
0%	0%	99.9%	0.1%	0%	0%	0%	0
100%	99.9%	0%	0.1%	0%	0%	0%	1

Compiler

Compiled 11 to 10 computations (9.1% saved)

sample1.4s (23.6%)

Memory

-2.8MiB live, 1 336.0MiB allocated

Samples

913.0ms

8 256×

valid

Precisions

Click to see histograms. Total time spent on operations: 440.0ms

ival-div: 258.0ms (58.7% of total)

ival-add: 88.0ms (20% of total)

ival-mult: 81.0ms (18.4% of total)

ival-true: 5.0ms (1.1% of total)

exact: 5.0ms (1.1% of total)

ival-assert: 3.0ms (0.7% of total)

Bogosity

preprocess70.0ms (1.2%)

Memory

31.5MiB live, 70.7MiB allocated

Algorithm

1×	egg-herbie

Rules

386×	`distribute-rgt-in`
336×	`sub-neg`
268×	`unsub-neg`
230×	`associate-+l-`
226×	`cancel-sign-sub`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	32	88
1	88	82
2	232	81
3	662	69
4	1166	65
5	1714	63
6	2190	63
7	2376	63
8	2424	63
9	2432	63
10	2432	63
0	8	9
0	12	9
1	17	9
2	24	9
3	26	9
0	26	8

Stop Event

1×	iter limit
1×	saturated
1×	iter limit
1×	saturated

Calls

Call 1

Inputs
(+.f64 (+.f64 (/.f64 x #s(literal 2 binary64)) (*.f64 y x)) z)

Outputs
(+.f64 (+.f64 (/.f64 x #s(literal 2 binary64)) (*.f64 y x)) z)
(+.f64 (/.f64 x #s(literal 2 binary64)) (fma.f64 x y z))

explain94.0ms (1.6%)

Memory

-11.1MiB live, 226.4MiB allocated

FPErrors

Click to see full error table

Example	Example	Subexpression
-	-	`(+.f64 (/.f64 x #s(literal 2 binary64)) (*.f64 y x))`
-	-	`#s(literal 2 binary64)`
-	-	`y`
-	-	`(/.f64 x #s(literal 2 binary64))`
-	-	`z`
-	-	`(+.f64 (+.f64 (/.f64 x #s(literal 2 binary64)) (*.f64 y x)) z)`
-	-	`(*.f64 y x)`
-	-	`x`

Confusion

	Predicted +	Predicted -
+	0	0
-	0	256

Precision

0/0

Recall

0/0

Confusion?

	Predicted +	Predicted Maybe	Predicted -
+	0	0	0
-	0	0	256

Precision?

0/0

Recall?

0/0

Freqs

test

number	freq
0	256

Total Confusion?

	Predicted +	Predicted Maybe	Predicted -
+	0	0	0
-	0	0	1

Precision?

0/0

Recall?

0/0

Samples

32.0ms

512×

valid

Compiler

Compiled 80 to 36 computations (55% saved)

Precisions

Click to see histograms. Total time spent on operations: 13.0ms

ival-add: 5.0ms (39.3% of total)

ival-mult: 4.0ms (31.5% of total)

ival-div: 3.0ms (23.6% of total)

ival-true: 0.0ms (0% of total)

exact: 0.0ms (0% of total)

ival-assert: 0.0ms (0% of total)

eval0.0ms (0%)

Memory: 0.5MiB live, 0.5MiB allocated
Compiler: Compiled 3 to 3 computations (0% saved)

prune1.0ms (0%)

Memory

2.1MiB live, 2.1MiB allocated

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	100.0%	(+.f64 (+.f64 (/.f64 x #s(literal 2 binary64)) (*.f64 y x)) z)

Compiler

Compiled 12 to 8 computations (33.3% saved)

simplify5.0ms (0.1%)

Memory

15.9MiB live, 15.9MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 4 expressions of interest:

New	Metric	Score	Program
✓	cost-diff	0	(*.f64 y x)
✓	cost-diff	0	(/.f64 x #s(literal 2 binary64))
✓	cost-diff	0	(+.f64 (+.f64 (/.f64 x #s(literal 2 binary64)) (*.f64 y x)) z)
✓	cost-diff	128	(+.f64 (/.f64 x #s(literal 2 binary64)) (*.f64 y x))

Rules

24×	`lower-+.f32`
20×	`lower-+.f64`
12×	`lower-fma.f64`
12×	`lower-fma.f32`
10×	`+-commutative`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	8	26
0	12	26
1	17	26
2	24	26
3	26	26
0	26	24

Stop Event

1×	iter limit
1×	saturated
1×	iter limit

Calls

Call 1

Inputs
(+.f64 (+.f64 (/.f64 x #s(literal 2 binary64)) (*.f64 y x)) z)
(+.f64 (/.f64 x #s(literal 2 binary64)) (*.f64 y x))
(/.f64 x #s(literal 2 binary64))
x
#s(literal 2 binary64)
(*.f64 y x)
y
z

Outputs
(+.f64 (+.f64 (/.f64 x #s(literal 2 binary64)) (*.f64 y x)) z)
(+.f64 (/.f64 x #s(literal 2 binary64)) (fma.f64 x y z))
(+.f64 (/.f64 x #s(literal 2 binary64)) (*.f64 y x))
(fma.f64 x y (/.f64 x #s(literal 2 binary64)))
(/.f64 x #s(literal 2 binary64))
x
#s(literal 2 binary64)
(*.f64 y x)
(*.f64 x y)
y
z

localize24.0ms (0.4%)

Memory

-22.4MiB live, 55.5MiB allocated

Localize:

Found 4 expressions of interest:

New	Metric	Score	Program
✓	accuracy	100.0%	(/.f64 x #s(literal 2 binary64))
✓	accuracy	100.0%	(*.f64 y x)
✓	accuracy	100.0%	(+.f64 (/.f64 x #s(literal 2 binary64)) (*.f64 y x))
✓	accuracy	100.0%	(+.f64 (+.f64 (/.f64 x #s(literal 2 binary64)) (*.f64 y x)) z)

Samples

16.0ms

256×

valid

Compiler

Compiled 28 to 10 computations (64.3% saved)

Precisions

Click to see histograms. Total time spent on operations: 7.0ms

ival-div: 3.0ms (43.4% of total)

ival-add: 2.0ms (28.9% of total)

ival-mult: 2.0ms (28.9% of total)

ival-true: 0.0ms (0% of total)

exact: 0.0ms (0% of total)

ival-assert: 0.0ms (0% of total)

series6.0ms (0.1%)

Memory

17.0MiB live, 17.0MiB allocated

Counts

4 → 96

Calls

Call 1

Inputs
#<alt (+.f64 (/.f64 x #s(literal 2 binary64)) (*.f64 y x))>
#<alt (+.f64 (+.f64 (/.f64 x #s(literal 2 binary64)) (*.f64 y x)) z)>
#<alt (/.f64 x #s(literal 2 binary64))>
#<alt (*.f64 y x)>

Outputs
#<alt (* x (+ 1/2 y))>
#<alt (* x (+ 1/2 y))>
#<alt (* x (+ 1/2 y))>
#<alt (* x (+ 1/2 y))>
#<alt (* x (+ 1/2 y))>
#<alt (* x (+ 1/2 y))>
#<alt (* x (+ 1/2 y))>
#<alt (* x (+ 1/2 y))>
#<alt (* -1 (* x (- (* -1 y) 1/2)))>
#<alt (* -1 (* x (- (* -1 y) 1/2)))>
#<alt (* -1 (* x (- (* -1 y) 1/2)))>
#<alt (* -1 (* x (- (* -1 y) 1/2)))>
#<alt (* 1/2 x)>
#<alt (+ (* 1/2 x) (* x y))>
#<alt (+ (* 1/2 x) (* x y))>
#<alt (+ (* 1/2 x) (* x y))>
#<alt (* x y)>
#<alt (* y (+ x (* 1/2 (/ x y))))>
#<alt (* y (+ x (* 1/2 (/ x y))))>
#<alt (* y (+ x (* 1/2 (/ x y))))>
#<alt (* x y)>
#<alt (* -1 (* y (+ (* -1 x) (* -1/2 (/ x y)))))>
#<alt (* -1 (* y (+ (* -1 x) (* -1/2 (/ x y)))))>
#<alt (* -1 (* y (+ (* -1 x) (* -1/2 (/ x y)))))>
#<alt z>
#<alt (+ z (* x (+ 1/2 y)))>
#<alt (+ z (* x (+ 1/2 y)))>
#<alt (+ z (* x (+ 1/2 y)))>
#<alt (* x (+ 1/2 y))>
#<alt (* x (+ 1/2 (+ y (/ z x))))>
#<alt (* x (+ 1/2 (+ y (/ z x))))>
#<alt (* x (+ 1/2 (+ y (/ z x))))>
#<alt (* -1 (* x (- (* -1 y) 1/2)))>
#<alt (* -1 (* x (- (+ (* -1 y) (* -1 (/ z x))) 1/2)))>
#<alt (* -1 (* x (- (+ (* -1 y) (* -1 (/ z x))) 1/2)))>
#<alt (* -1 (* x (- (+ (* -1 y) (* -1 (/ z x))) 1/2)))>
#<alt (+ z (* 1/2 x))>
#<alt (+ z (+ (* 1/2 x) (* x y)))>
#<alt (+ z (+ (* 1/2 x) (* x y)))>
#<alt (+ z (+ (* 1/2 x) (* x y)))>
#<alt (* x y)>
#<alt (* y (+ x (+ (* 1/2 (/ x y)) (/ z y))))>
#<alt (* y (+ x (+ (* 1/2 (/ x y)) (/ z y))))>
#<alt (* y (+ x (+ (* 1/2 (/ x y)) (/ z y))))>
#<alt (* x y)>
#<alt (* -1 (* y (+ (* -1 x) (* -1 (/ (+ z (* 1/2 x)) y)))))>
#<alt (* -1 (* y (+ (* -1 x) (* -1 (/ (+ z (* 1/2 x)) y)))))>
#<alt (* -1 (* y (+ (* -1 x) (* -1 (/ (+ z (* 1/2 x)) y)))))>
#<alt (+ (* 1/2 x) (* x y))>
#<alt (+ z (+ (* 1/2 x) (* x y)))>
#<alt (+ z (+ (* 1/2 x) (* x y)))>
#<alt (+ z (+ (* 1/2 x) (* x y)))>
#<alt z>
#<alt (* z (+ 1 (+ (* 1/2 (/ x z)) (/ (* x y) z))))>
#<alt (* z (+ 1 (+ (* 1/2 (/ x z)) (/ (* x y) z))))>
#<alt (* z (+ 1 (+ (* 1/2 (/ x z)) (/ (* x y) z))))>
#<alt z>
#<alt (* -1 (* z (- (* -1 (/ (+ (* 1/2 x) (* x y)) z)) 1)))>
#<alt (* -1 (* z (- (* -1 (/ (+ (* 1/2 x) (* x y)) z)) 1)))>
#<alt (* -1 (* z (- (* -1 (/ (+ (* 1/2 x) (* x y)) z)) 1)))>
#<alt (* 1/2 x)>
#<alt (* 1/2 x)>
#<alt (* 1/2 x)>
#<alt (* 1/2 x)>
#<alt (* 1/2 x)>
#<alt (* 1/2 x)>
#<alt (* 1/2 x)>
#<alt (* 1/2 x)>
#<alt (* 1/2 x)>
#<alt (* 1/2 x)>
#<alt (* 1/2 x)>
#<alt (* 1/2 x)>
#<alt (* x y)>
#<alt (* x y)>
#<alt (* x y)>
#<alt (* x y)>
#<alt (* x y)>
#<alt (* x y)>
#<alt (* x y)>
#<alt (* x y)>
#<alt (* x y)>
#<alt (* x y)>
#<alt (* x y)>
#<alt (* x y)>
#<alt (* x y)>
#<alt (* x y)>
#<alt (* x y)>
#<alt (* x y)>
#<alt (* x y)>
#<alt (* x y)>
#<alt (* x y)>
#<alt (* x y)>
#<alt (* x y)>
#<alt (* x y)>
#<alt (* x y)>
#<alt (* x y)>

Calls

24 calls:

Time	Variable		Point	Expression
1.0ms	x	@	inf	(+ (/ x 2) (* y x))
1.0ms	x	@	-inf	(/ x 2)
1.0ms	x	@	0	(+ (/ x 2) (* y x))
1.0ms	x	@	-inf	(+ (/ x 2) (* y x))
0.0ms	y	@	0	(+ (/ x 2) (* y x))

rewrite327.0ms (5.4%)

Memory

8.6MiB live, 555.5MiB allocated

Algorithm

1×	batch-egg-rewrite

Rules

7 074×	`lower-fma.f64`
7 074×	`lower-fma.f32`
4 356×	`lower-*.f32`
4 354×	`lower-*.f64`
2 578×	`lower-/.f32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	8	22
0	12	22
1	52	18
2	452	18
3	6077	18
0	8040	17

Stop Event

1×	iter limit
1×	node limit
1×	iter limit

Counts

4 → 242

Calls

Call 1

Inputs
(+.f64 (/.f64 x #s(literal 2 binary64)) (*.f64 y x))
(+.f64 (+.f64 (/.f64 x #s(literal 2 binary64)) (*.f64 y x)) z)
(/.f64 x #s(literal 2 binary64))
(*.f64 y x)

Outputs
(+.f64 (.f64 x #s(literal 1/2 binary64)) (.f64 x y))
(+.f64 (.f64 x y) (.f64 x #s(literal 1/2 binary64)))
(+.f64 (/.f64 (.f64 x (.f64 #s(literal 1/4 binary64) x)) (.f64 x (-.f64 #s(literal 1/2 binary64) y))) (neg.f64 (/.f64 (.f64 x (.f64 x (.f64 y y))) (*.f64 x (-.f64 #s(literal 1/2 binary64) y)))))
(exp.f64 (.f64 (log.f64 (.f64 x (+.f64 y #s(literal 1/2 binary64)))) #s(literal 1 binary64)))
(exp.f64 (.f64 (neg.f64 (log.f64 (.f64 x (+.f64 y #s(literal 1/2 binary64))))) #s(literal -1 binary64)))
(-.f64 (.f64 x y) (.f64 x #s(literal -1/2 binary64)))
(-.f64 (/.f64 (.f64 x (.f64 #s(literal 1/4 binary64) x)) (.f64 x (-.f64 #s(literal 1/2 binary64) y))) (/.f64 (.f64 x (.f64 x (.f64 y y))) (*.f64 x (-.f64 #s(literal 1/2 binary64) y))))
(-.f64 (/.f64 (.f64 x (.f64 x (.f64 y y))) (.f64 x (-.f64 y #s(literal 1/2 binary64)))) (/.f64 (.f64 x (.f64 #s(literal 1/4 binary64) x)) (*.f64 x (-.f64 y #s(literal 1/2 binary64)))))
(fma.f64 x y (*.f64 x #s(literal 1/2 binary64)))
(fma.f64 x #s(literal 1/2 binary64) (*.f64 x y))
(fma.f64 x (/.f64 (.f64 #s(literal 1/4 binary64) x) (.f64 x (-.f64 #s(literal 1/2 binary64) y))) (neg.f64 (/.f64 (.f64 x (.f64 x (.f64 y y))) (.f64 x (-.f64 #s(literal 1/2 binary64) y)))))
(fma.f64 (.f64 x #s(literal 1/2 binary64)) #s(literal 1 binary64) (.f64 x y))
(fma.f64 (.f64 x #s(literal 1/2 binary64)) (/.f64 (.f64 x #s(literal 1/2 binary64)) (.f64 x (-.f64 #s(literal 1/2 binary64) y))) (neg.f64 (/.f64 (.f64 x (.f64 x (.f64 y y))) (*.f64 x (-.f64 #s(literal 1/2 binary64) y)))))
(fma.f64 y x (*.f64 x #s(literal 1/2 binary64)))
(fma.f64 (.f64 x y) #s(literal 1 binary64) (.f64 x #s(literal 1/2 binary64)))
(fma.f64 (neg.f64 x) #s(literal -1/2 binary64) (*.f64 x y))
(fma.f64 (.f64 x (.f64 #s(literal 1/4 binary64) x)) (/.f64 #s(literal 1 binary64) (.f64 x (-.f64 #s(literal 1/2 binary64) y))) (neg.f64 (/.f64 (.f64 x (.f64 x (.f64 y y))) (*.f64 x (-.f64 #s(literal 1/2 binary64) y)))))
(fma.f64 #s(literal 1 binary64) (.f64 x #s(literal 1/2 binary64)) (.f64 x y))
(fma.f64 #s(literal 1 binary64) (.f64 x y) (.f64 x #s(literal 1/2 binary64)))
(fma.f64 #s(literal 1/2 binary64) x (*.f64 x y))
(fma.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) x)) (*.f64 x y))
(fma.f64 #s(literal -1 binary64) (.f64 x #s(literal -1/2 binary64)) (.f64 x y))
(fma.f64 #s(literal -1/2 binary64) (neg.f64 x) (*.f64 x y))
(fma.f64 (.f64 x (.f64 x #s(literal 1/2 binary64))) (/.f64 #s(literal 1/2 binary64) (.f64 x (-.f64 #s(literal 1/2 binary64) y))) (neg.f64 (/.f64 (.f64 x (.f64 x (.f64 y y))) (*.f64 x (-.f64 #s(literal 1/2 binary64) y)))))
(fma.f64 (.f64 x x) (/.f64 #s(literal 1/4 binary64) (.f64 x (-.f64 #s(literal 1/2 binary64) y))) (neg.f64 (/.f64 (.f64 x (.f64 x (.f64 y y))) (.f64 x (-.f64 #s(literal 1/2 binary64) y)))))
(fma.f64 (/.f64 x x) (/.f64 (.f64 #s(literal 1/4 binary64) x) (-.f64 #s(literal 1/2 binary64) y)) (neg.f64 (/.f64 (.f64 x (.f64 x (.f64 y y))) (*.f64 x (-.f64 #s(literal 1/2 binary64) y)))))
(fma.f64 (/.f64 (.f64 x x) x) (/.f64 #s(literal 1/4 binary64) (-.f64 #s(literal 1/2 binary64) y)) (neg.f64 (/.f64 (.f64 x (.f64 x (.f64 y y))) (*.f64 x (-.f64 #s(literal 1/2 binary64) y)))))
(fma.f64 (/.f64 (.f64 x #s(literal 1/2 binary64)) x) (/.f64 (.f64 x #s(literal 1/2 binary64)) (-.f64 #s(literal 1/2 binary64) y)) (neg.f64 (/.f64 (.f64 x (.f64 x (.f64 y y))) (.f64 x (-.f64 #s(literal 1/2 binary64) y)))))
(fma.f64 (/.f64 (.f64 x (.f64 x #s(literal 1/2 binary64))) x) (/.f64 #s(literal 1/2 binary64) (-.f64 #s(literal 1/2 binary64) y)) (neg.f64 (/.f64 (.f64 x (.f64 x (.f64 y y))) (.f64 x (-.f64 #s(literal 1/2 binary64) y)))))
(fma.f64 (pow.f64 (.f64 x #s(literal 1/2 binary64)) #s(literal 1/2 binary64)) (pow.f64 (.f64 x #s(literal 1/2 binary64)) #s(literal 1/2 binary64)) (*.f64 x y))
(fma.f64 (.f64 #s(literal 1 binary64) y) x (.f64 x #s(literal 1/2 binary64)))
(fma.f64 (/.f64 (.f64 x (.f64 #s(literal 1/4 binary64) x)) (.f64 (.f64 x x) (-.f64 #s(literal 1/4 binary64) (.f64 y y)))) (.f64 x (+.f64 y #s(literal 1/2 binary64))) (neg.f64 (/.f64 (.f64 x (.f64 x (.f64 y y))) (.f64 x (-.f64 #s(literal 1/2 binary64) y)))))
(fma.f64 (/.f64 (.f64 x (.f64 #s(literal 1/4 binary64) x)) (.f64 (.f64 x (.f64 x x)) (-.f64 #s(literal 1/8 binary64) (.f64 y (.f64 y y))))) (fma.f64 x (.f64 #s(literal 1/4 binary64) x) (.f64 (.f64 x (.f64 x y)) (+.f64 y #s(literal 1/2 binary64)))) (neg.f64 (/.f64 (.f64 x (.f64 x (.f64 y y))) (*.f64 x (-.f64 #s(literal 1/2 binary64) y)))))
(neg.f64 (*.f64 (neg.f64 x) (+.f64 y #s(literal 1/2 binary64))))
(/.f64 (.f64 (.f64 x (.f64 x x)) (fma.f64 y (.f64 y y) #s(literal 1/8 binary64))) (fma.f64 x (.f64 y (.f64 x (-.f64 y #s(literal 1/2 binary64)))) (.f64 x (.f64 #s(literal 1/4 binary64) x))))
(/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (*.f64 x (+.f64 y #s(literal 1/2 binary64)))))
(/.f64 #s(literal 1 binary64) (/.f64 (/.f64 #s(literal 1 binary64) (*.f64 x (+.f64 y #s(literal 1/2 binary64)))) #s(literal 1 binary64)))
(/.f64 #s(literal 1 binary64) (/.f64 (.f64 x (-.f64 y #s(literal 1/2 binary64))) (.f64 (.f64 x x) (-.f64 (.f64 y y) #s(literal 1/4 binary64)))))
(/.f64 (.f64 (.f64 x x) (-.f64 #s(literal 1/4 binary64) (.f64 y y))) (.f64 x (-.f64 #s(literal 1/2 binary64) y)))
(/.f64 #s(literal -1 binary64) (neg.f64 (/.f64 #s(literal 1 binary64) (*.f64 x (+.f64 y #s(literal 1/2 binary64))))))
(/.f64 (neg.f64 (.f64 (.f64 x (.f64 x x)) (fma.f64 y (.f64 y y) #s(literal 1/8 binary64)))) (neg.f64 (fma.f64 x (.f64 y (.f64 x (-.f64 y #s(literal 1/2 binary64)))) (.f64 x (.f64 #s(literal 1/4 binary64) x)))))
(/.f64 (neg.f64 (.f64 (.f64 x x) (-.f64 #s(literal 1/4 binary64) (.f64 y y)))) (.f64 (neg.f64 x) (-.f64 #s(literal 1/2 binary64) y)))
(/.f64 (.f64 (fma.f64 (.f64 (.f64 x (.f64 y y)) (.f64 x (.f64 x y))) (-.f64 (.f64 (.f64 x (.f64 y y)) (.f64 x (.f64 x y))) (.f64 (.f64 x (.f64 x x)) #s(literal 1/8 binary64))) (.f64 (.f64 (.f64 x (.f64 x x)) (.f64 x (.f64 x x))) #s(literal 1/64 binary64))) (.f64 (.f64 x (.f64 x x)) (fma.f64 y (.f64 y y) #s(literal 1/8 binary64)))) (.f64 (fma.f64 x (.f64 y (.f64 x (-.f64 y #s(literal 1/2 binary64)))) (.f64 x (.f64 #s(literal 1/4 binary64) x))) (fma.f64 (.f64 (.f64 x (.f64 y y)) (.f64 x (.f64 x y))) (-.f64 (.f64 (.f64 x (.f64 y y)) (.f64 x (.f64 x y))) (.f64 (.f64 x (.f64 x x)) #s(literal 1/8 binary64))) (.f64 (.f64 (.f64 x (.f64 x x)) (.f64 x (.f64 x x))) #s(literal 1/64 binary64)))))
(/.f64 (.f64 (.f64 (.f64 x (.f64 x x)) (fma.f64 y (.f64 y y) #s(literal 1/8 binary64))) (.f64 (.f64 x (.f64 x x)) (-.f64 #s(literal 1/8 binary64) (.f64 y (.f64 y y))))) (.f64 (fma.f64 x (.f64 y (.f64 x (-.f64 y #s(literal 1/2 binary64)))) (.f64 x (.f64 #s(literal 1/4 binary64) x))) (.f64 (.f64 x (.f64 x x)) (-.f64 #s(literal 1/8 binary64) (.f64 y (.f64 y y))))))
(/.f64 (.f64 (.f64 (.f64 x (.f64 x x)) (fma.f64 y (.f64 y y) #s(literal 1/8 binary64))) (.f64 (.f64 x (.f64 x x)) (-.f64 #s(literal 1/8 binary64) (.f64 y (.f64 y y))))) (.f64 (.f64 x (-.f64 #s(literal 1/2 binary64) y)) (fma.f64 (.f64 x (.f64 x (.f64 y y))) (.f64 (.f64 x x) (+.f64 #s(literal 1/4 binary64) (.f64 y y))) (.f64 (.f64 (.f64 x x) (.f64 x x)) #s(literal 1/16 binary64)))))
(/.f64 (.f64 (.f64 x x) (-.f64 (.f64 y y) #s(literal 1/4 binary64))) (.f64 x (-.f64 y #s(literal 1/2 binary64))))
(/.f64 (.f64 (.f64 (.f64 x x) (+.f64 #s(literal 1/4 binary64) (.f64 y y))) (.f64 (.f64 x x) (-.f64 #s(literal 1/4 binary64) (.f64 y y)))) (.f64 (.f64 x (-.f64 #s(literal 1/2 binary64) y)) (.f64 (.f64 x x) (+.f64 #s(literal 1/4 binary64) (.f64 y y)))))
(/.f64 (-.f64 (.f64 (.f64 x (.f64 #s(literal 1/4 binary64) x)) (.f64 x (-.f64 #s(literal 1/2 binary64) y))) (.f64 (.f64 x (-.f64 #s(literal 1/2 binary64) y)) (.f64 x (.f64 x (.f64 y y))))) (.f64 x (.f64 (-.f64 #s(literal 1/2 binary64) y) (.f64 x (-.f64 #s(literal 1/2 binary64) y)))))
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(/.f64 (-.f64 (.f64 (/.f64 (.f64 x (.f64 (+.f64 y #s(literal 1/2 binary64)) (.f64 x (+.f64 y #s(literal 1/2 binary64))))) (fma.f64 x (+.f64 y #s(literal 1/2 binary64)) (neg.f64 z))) (/.f64 (.f64 x (.f64 (+.f64 y #s(literal 1/2 binary64)) (.f64 x (+.f64 y #s(literal 1/2 binary64))))) (fma.f64 x (+.f64 y #s(literal 1/2 binary64)) (neg.f64 z)))) (.f64 (/.f64 (.f64 z z) (fma.f64 x (+.f64 y #s(literal 1/2 binary64)) (neg.f64 z))) (/.f64 (.f64 z z) (fma.f64 x (+.f64 y #s(literal 1/2 binary64)) (neg.f64 z))))) (fma.f64 (.f64 x (+.f64 y #s(literal 1/2 binary64))) (/.f64 (.f64 x (+.f64 y #s(literal 1/2 binary64))) (fma.f64 x (+.f64 y #s(literal 1/2 binary64)) (neg.f64 z))) (/.f64 (*.f64 z z) (fma.f64 x (+.f64 y #s(literal 1/2 binary64)) (neg.f64 z)))))
(/.f64 (.f64 (.f64 (fma.f64 x (+.f64 y #s(literal 1/2 binary64)) z) (fma.f64 (.f64 x (+.f64 y #s(literal 1/2 binary64))) (fma.f64 x (+.f64 y #s(literal 1/2 binary64)) (neg.f64 z)) (.f64 z z))) #s(literal 1 binary64)) (fma.f64 (.f64 x (+.f64 y #s(literal 1/2 binary64))) (fma.f64 x (+.f64 y #s(literal 1/2 binary64)) (neg.f64 z)) (.f64 z z)))
(/.f64 (.f64 (.f64 (fma.f64 x (+.f64 y #s(literal 1/2 binary64)) z) (fma.f64 x (+.f64 y #s(literal 1/2 binary64)) (neg.f64 z))) #s(literal 1 binary64)) (fma.f64 x (+.f64 y #s(literal 1/2 binary64)) (neg.f64 z)))
(/.f64 (.f64 (fma.f64 (.f64 z (.f64 z z)) (.f64 (.f64 z (.f64 z z)) (.f64 z (.f64 z z))) (pow.f64 (.f64 x (+.f64 y #s(literal 1/2 binary64))) #s(literal 9 binary64))) (/.f64 #s(literal 1 binary64) (fma.f64 (.f64 x (+.f64 y #s(literal 1/2 binary64))) (fma.f64 x (+.f64 y #s(literal 1/2 binary64)) (neg.f64 z)) (.f64 z z)))) (fma.f64 (.f64 x (+.f64 y #s(literal 1/2 binary64))) (.f64 (.f64 x (.f64 (+.f64 y #s(literal 1/2 binary64)) (.f64 x (+.f64 y #s(literal 1/2 binary64))))) (.f64 (.f64 x (+.f64 y #s(literal 1/2 binary64))) (.f64 x (.f64 (+.f64 y #s(literal 1/2 binary64)) (.f64 x (+.f64 y #s(literal 1/2 binary64))))))) (.f64 (.f64 z (.f64 z z)) (-.f64 (.f64 z (.f64 z z)) (.f64 (.f64 x (+.f64 y #s(literal 1/2 binary64))) (.f64 x (.f64 (+.f64 y #s(literal 1/2 binary64)) (*.f64 x (+.f64 y #s(literal 1/2 binary64))))))))))
(/.f64 (.f64 (.f64 (.f64 (fma.f64 x (+.f64 y #s(literal 1/2 binary64)) z) (fma.f64 (.f64 x (+.f64 y #s(literal 1/2 binary64))) (fma.f64 x (+.f64 y #s(literal 1/2 binary64)) (neg.f64 z)) (.f64 z z))) (-.f64 (.f64 (.f64 x (+.f64 y #s(literal 1/2 binary64))) (.f64 x (.f64 (+.f64 y #s(literal 1/2 binary64)) (.f64 x (+.f64 y #s(literal 1/2 binary64)))))) (.f64 z (.f64 z z)))) (/.f64 #s(literal 1 binary64) (fma.f64 (.f64 x (+.f64 y #s(literal 1/2 binary64))) (fma.f64 x (+.f64 y #s(literal 1/2 binary64)) (neg.f64 z)) (.f64 z z)))) (-.f64 (.f64 (.f64 x (+.f64 y #s(literal 1/2 binary64))) (.f64 x (.f64 (+.f64 y #s(literal 1/2 binary64)) (.f64 x (+.f64 y #s(literal 1/2 binary64)))))) (.f64 z (*.f64 z z))))
(/.f64 (.f64 (.f64 (.f64 (fma.f64 x (+.f64 y #s(literal 1/2 binary64)) z) (fma.f64 (.f64 x (+.f64 y #s(literal 1/2 binary64))) (fma.f64 x (+.f64 y #s(literal 1/2 binary64)) (neg.f64 z)) (.f64 z z))) (-.f64 (.f64 (.f64 x (+.f64 y #s(literal 1/2 binary64))) (.f64 x (.f64 (+.f64 y #s(literal 1/2 binary64)) (.f64 x (+.f64 y #s(literal 1/2 binary64)))))) (.f64 z (.f64 z z)))) (/.f64 #s(literal 1 binary64) (fma.f64 x (+.f64 y #s(literal 1/2 binary64)) (neg.f64 z)))) (fma.f64 (.f64 x (+.f64 y #s(literal 1/2 binary64))) (.f64 (.f64 x (+.f64 y #s(literal 1/2 binary64))) (.f64 x (.f64 (+.f64 y #s(literal 1/2 binary64)) (.f64 x (+.f64 y #s(literal 1/2 binary64)))))) (.f64 (.f64 z z) (fma.f64 (.f64 x (+.f64 y #s(literal 1/2 binary64))) (.f64 x (+.f64 y #s(literal 1/2 binary64))) (*.f64 z z)))))
(/.f64 (.f64 (.f64 (fma.f64 (.f64 x (+.f64 y #s(literal 1/2 binary64))) (.f64 x (+.f64 y #s(literal 1/2 binary64))) (.f64 z z)) (.f64 (fma.f64 x (+.f64 y #s(literal 1/2 binary64)) z) (fma.f64 x (+.f64 y #s(literal 1/2 binary64)) (neg.f64 z)))) (/.f64 #s(literal 1 binary64) (fma.f64 x (+.f64 y #s(literal 1/2 binary64)) (neg.f64 z)))) (fma.f64 (.f64 x (+.f64 y #s(literal 1/2 binary64))) (.f64 x (+.f64 y #s(literal 1/2 binary64))) (*.f64 z z)))
(pow.f64 (/.f64 #s(literal 1 binary64) (fma.f64 x (+.f64 y #s(literal 1/2 binary64)) z)) #s(literal -1 binary64))
(pow.f64 (/.f64 (/.f64 #s(literal 1 binary64) (fma.f64 x (+.f64 y #s(literal 1/2 binary64)) z)) #s(literal 1 binary64)) #s(literal -1 binary64))
(pow.f64 (/.f64 (fma.f64 x (.f64 #s(literal 1/4 binary64) x) (.f64 (fma.f64 x y z) (-.f64 (fma.f64 x y z) (.f64 x #s(literal 1/2 binary64))))) (fma.f64 (fma.f64 x y z) (.f64 (fma.f64 x y z) (fma.f64 x y z)) (.f64 (.f64 x (*.f64 x x)) #s(literal 1/8 binary64)))) #s(literal -1 binary64))
(pow.f64 (/.f64 (-.f64 (.f64 x (-.f64 #s(literal 1/2 binary64) y)) z) (.f64 (fma.f64 x (+.f64 y #s(literal 1/2 binary64)) z) (-.f64 (*.f64 x (-.f64 #s(literal 1/2 binary64) y)) z))) #s(literal -1 binary64))
(pow.f64 (/.f64 (-.f64 z (.f64 x (+.f64 y #s(literal 1/2 binary64)))) (.f64 (fma.f64 x (+.f64 y #s(literal 1/2 binary64)) z) (-.f64 z (*.f64 x (+.f64 y #s(literal 1/2 binary64)))))) #s(literal -1 binary64))
(.f64 (fma.f64 x (+.f64 y #s(literal 1/2 binary64)) z) (.f64 (fma.f64 x (+.f64 y #s(literal 1/2 binary64)) (neg.f64 z)) (/.f64 #s(literal 1 binary64) (fma.f64 x (+.f64 y #s(literal 1/2 binary64)) (neg.f64 z)))))
(*.f64 (fma.f64 x (+.f64 y #s(literal 1/2 binary64)) z) (/.f64 (fma.f64 x (+.f64 y #s(literal 1/2 binary64)) (neg.f64 z)) (fma.f64 x (+.f64 y #s(literal 1/2 binary64)) (neg.f64 z))))
(.f64 (.f64 (fma.f64 x (+.f64 y #s(literal 1/2 binary64)) z) (fma.f64 (.f64 x (+.f64 y #s(literal 1/2 binary64))) (fma.f64 x (+.f64 y #s(literal 1/2 binary64)) (neg.f64 z)) (.f64 z z))) (/.f64 #s(literal 1 binary64) (fma.f64 (.f64 x (+.f64 y #s(literal 1/2 binary64))) (fma.f64 x (+.f64 y #s(literal 1/2 binary64)) (neg.f64 z)) (.f64 z z))))
(.f64 (fma.f64 (.f64 x (+.f64 y #s(literal 1/2 binary64))) (fma.f64 x (+.f64 y #s(literal 1/2 binary64)) (neg.f64 z)) (.f64 z z)) (.f64 (fma.f64 x (+.f64 y #s(literal 1/2 binary64)) z) (/.f64 #s(literal 1 binary64) (fma.f64 (.f64 x (+.f64 y #s(literal 1/2 binary64))) (fma.f64 x (+.f64 y #s(literal 1/2 binary64)) (neg.f64 z)) (.f64 z z)))))
(.f64 (fma.f64 (.f64 x (+.f64 y #s(literal 1/2 binary64))) (fma.f64 x (+.f64 y #s(literal 1/2 binary64)) (neg.f64 z)) (.f64 z z)) (/.f64 (fma.f64 x (+.f64 y #s(literal 1/2 binary64)) z) (fma.f64 (.f64 x (+.f64 y #s(literal 1/2 binary64))) (fma.f64 x (+.f64 y #s(literal 1/2 binary64)) (neg.f64 z)) (*.f64 z z))))
(*.f64 #s(literal 1 binary64) (fma.f64 x (+.f64 y #s(literal 1/2 binary64)) z))
(.f64 (.f64 (fma.f64 x (+.f64 y #s(literal 1/2 binary64)) z) (fma.f64 x (+.f64 y #s(literal 1/2 binary64)) (neg.f64 z))) (/.f64 #s(literal 1 binary64) (fma.f64 x (+.f64 y #s(literal 1/2 binary64)) (neg.f64 z))))
(.f64 (neg.f64 (.f64 (fma.f64 x (+.f64 y #s(literal 1/2 binary64)) z) (fma.f64 (.f64 x (+.f64 y #s(literal 1/2 binary64))) (fma.f64 x (+.f64 y #s(literal 1/2 binary64)) (neg.f64 z)) (.f64 z z)))) (/.f64 #s(literal 1 binary64) (neg.f64 (fma.f64 (.f64 x (+.f64 y #s(literal 1/2 binary64))) (fma.f64 x (+.f64 y #s(literal 1/2 binary64)) (neg.f64 z)) (.f64 z z)))))
(.f64 (neg.f64 (.f64 (fma.f64 x (+.f64 y #s(literal 1/2 binary64)) z) (fma.f64 x (+.f64 y #s(literal 1/2 binary64)) (neg.f64 z)))) (/.f64 #s(literal 1 binary64) (neg.f64 (fma.f64 x (+.f64 y #s(literal 1/2 binary64)) (neg.f64 z)))))
(.f64 (fma.f64 (fma.f64 x y z) (.f64 (fma.f64 x y z) (fma.f64 x y z)) (.f64 (.f64 x (.f64 x x)) #s(literal 1/8 binary64))) (/.f64 #s(literal 1 binary64) (fma.f64 x (.f64 #s(literal 1/4 binary64) x) (.f64 (fma.f64 x y z) (-.f64 (fma.f64 x y z) (.f64 x #s(literal 1/2 binary64)))))))
(.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (.f64 x (+.f64 y #s(literal 1/2 binary64))) (fma.f64 x (+.f64 y #s(literal 1/2 binary64)) (neg.f64 z)) (.f64 z z))) (.f64 (fma.f64 x (+.f64 y #s(literal 1/2 binary64)) z) (fma.f64 (.f64 x (+.f64 y #s(literal 1/2 binary64))) (fma.f64 x (+.f64 y #s(literal 1/2 binary64)) (neg.f64 z)) (.f64 z z))))
(.f64 (/.f64 #s(literal 1 binary64) (fma.f64 x (+.f64 y #s(literal 1/2 binary64)) (neg.f64 z))) (.f64 (fma.f64 x (+.f64 y #s(literal 1/2 binary64)) z) (fma.f64 x (+.f64 y #s(literal 1/2 binary64)) (neg.f64 z))))
(.f64 (.f64 (fma.f64 x (+.f64 y #s(literal 1/2 binary64)) z) (-.f64 (.f64 x (-.f64 #s(literal 1/2 binary64) y)) z)) (/.f64 #s(literal 1 binary64) (-.f64 (.f64 x (-.f64 #s(literal 1/2 binary64) y)) z)))
(.f64 (.f64 (fma.f64 x (+.f64 y #s(literal 1/2 binary64)) z) (-.f64 z (.f64 x (+.f64 y #s(literal 1/2 binary64))))) (/.f64 #s(literal 1 binary64) (-.f64 z (.f64 x (+.f64 y #s(literal 1/2 binary64))))))
(.f64 (/.f64 (.f64 (fma.f64 x (+.f64 y #s(literal 1/2 binary64)) z) (fma.f64 x (+.f64 y #s(literal 1/2 binary64)) (neg.f64 z))) (*.f64 (fma.f64 x (+.f64 y #s(literal 1/2 binary64)) z) (fma.f64 x (+.f64 y #s(literal 1/2 binary64)) (neg.f64 z)))) (fma.f64 x (+.f64 y #s(literal 1/2 binary64)) z))
(.f64 (/.f64 (.f64 (fma.f64 x (+.f64 y #s(literal 1/2 binary64)) z) (fma.f64 (.f64 x (+.f64 y #s(literal 1/2 binary64))) (fma.f64 x (+.f64 y #s(literal 1/2 binary64)) (neg.f64 z)) (.f64 z z))) (fma.f64 (.f64 z (-.f64 z (.f64 x (+.f64 y #s(literal 1/2 binary64))))) (.f64 z (.f64 (-.f64 z (.f64 x (+.f64 y #s(literal 1/2 binary64)))) (.f64 z (-.f64 z (.f64 x (+.f64 y #s(literal 1/2 binary64))))))) (.f64 (.f64 (.f64 x (+.f64 y #s(literal 1/2 binary64))) (.f64 x (.f64 (+.f64 y #s(literal 1/2 binary64)) (.f64 x (+.f64 y #s(literal 1/2 binary64)))))) (.f64 (.f64 x (+.f64 y #s(literal 1/2 binary64))) (.f64 x (.f64 (+.f64 y #s(literal 1/2 binary64)) (.f64 x (+.f64 y #s(literal 1/2 binary64))))))))) (fma.f64 (.f64 z (-.f64 z (.f64 x (+.f64 y #s(literal 1/2 binary64))))) (-.f64 (.f64 z (-.f64 z (.f64 x (+.f64 y #s(literal 1/2 binary64))))) (.f64 x (.f64 (+.f64 y #s(literal 1/2 binary64)) (.f64 x (+.f64 y #s(literal 1/2 binary64)))))) (.f64 (.f64 x (.f64 (+.f64 y #s(literal 1/2 binary64)) (.f64 x (+.f64 y #s(literal 1/2 binary64))))) (.f64 x (.f64 (+.f64 y #s(literal 1/2 binary64)) (.f64 x (+.f64 y #s(literal 1/2 binary64))))))))
(.f64 (/.f64 (.f64 (fma.f64 x (+.f64 y #s(literal 1/2 binary64)) z) (fma.f64 (.f64 x (+.f64 y #s(literal 1/2 binary64))) (fma.f64 x (+.f64 y #s(literal 1/2 binary64)) (neg.f64 z)) (.f64 z z))) (.f64 (fma.f64 (.f64 x (+.f64 y #s(literal 1/2 binary64))) (fma.f64 x (+.f64 y #s(literal 1/2 binary64)) (neg.f64 z)) (.f64 z z)) (fma.f64 (fma.f64 x (+.f64 y #s(literal 1/2 binary64)) z) (fma.f64 x (+.f64 y #s(literal 1/2 binary64)) (neg.f64 z)) (.f64 x (.f64 (+.f64 y #s(literal 1/2 binary64)) z))))) (fma.f64 (fma.f64 x (+.f64 y #s(literal 1/2 binary64)) z) (fma.f64 x (+.f64 y #s(literal 1/2 binary64)) (neg.f64 z)) (.f64 x (*.f64 (+.f64 y #s(literal 1/2 binary64)) z))))
(.f64 (/.f64 (.f64 (fma.f64 x (+.f64 y #s(literal 1/2 binary64)) z) (fma.f64 x (+.f64 y #s(literal 1/2 binary64)) (neg.f64 z))) (-.f64 (.f64 (.f64 x (+.f64 y #s(literal 1/2 binary64))) (.f64 x (.f64 (+.f64 y #s(literal 1/2 binary64)) (.f64 x (+.f64 y #s(literal 1/2 binary64)))))) (.f64 z (.f64 z z)))) (fma.f64 x (.f64 (+.f64 y #s(literal 1/2 binary64)) (.f64 x (+.f64 y #s(literal 1/2 binary64)))) (.f64 z (fma.f64 x (+.f64 y #s(literal 1/2 binary64)) z))))
(exp.f64 (.f64 (neg.f64 (log.f64 (.f64 x #s(literal 1/2 binary64)))) #s(literal -1 binary64)))
(exp.f64 (.f64 (log.f64 (.f64 x #s(literal 1/2 binary64))) #s(literal 1 binary64)))
(-.f64 #s(literal 0 binary64) (*.f64 x #s(literal -1/2 binary64)))
(neg.f64 (*.f64 x #s(literal -1/2 binary64)))
(neg.f64 (.f64 (.f64 x #s(literal -1/2 binary64)) #s(literal 1 binary64)))
(/.f64 x #s(literal 2 binary64))
(/.f64 (neg.f64 x) #s(literal -2 binary64))
(/.f64 #s(literal 1 binary64) (/.f64 #s(literal 2 binary64) x))
(/.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1 binary64) x))
(/.f64 #s(literal -1 binary64) (/.f64 #s(literal -2 binary64) x))
(pow.f64 (*.f64 x #s(literal 1/2 binary64)) #s(literal 1 binary64))
(pow.f64 (/.f64 #s(literal 2 binary64) x) #s(literal -1 binary64))
(*.f64 x #s(literal 1/2 binary64))
(.f64 (.f64 x #s(literal 1/2 binary64)) #s(literal 1 binary64))
(*.f64 (neg.f64 x) #s(literal -1/2 binary64))
(.f64 #s(literal 1 binary64) (.f64 x #s(literal 1/2 binary64)))
(*.f64 #s(literal 1/2 binary64) x)
(*.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) x)))
(.f64 #s(literal -1 binary64) (.f64 x #s(literal -1/2 binary64)))
(*.f64 #s(literal -1/2 binary64) (neg.f64 x))
(.f64 (pow.f64 (.f64 x #s(literal 1/2 binary64)) #s(literal 1/2 binary64)) (pow.f64 (*.f64 x #s(literal 1/2 binary64)) #s(literal 1/2 binary64)))
(*.f64 x y)
(*.f64 y x)
(.f64 (.f64 x y) #s(literal 1 binary64))
(.f64 #s(literal 1 binary64) (.f64 x y))
(.f64 (.f64 #s(literal 1 binary64) y) x)

simplify209.0ms (3.5%)

Memory

-36.1MiB live, 305.6MiB allocated

Algorithm

1×	egg-herbie

Rules

6 434×	`lower-fma.f64`
6 434×	`lower-fma.f32`
2 474×	`lower-*.f64`
2 474×	`lower-*.f32`
1 356×	`lower-/.f32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	57	440
1	174	440
2	488	440
3	1310	440
4	3612	440
5	6659	440
0	8189	412

Stop Event

1×	iter limit
1×	node limit

Counts

96 → 93

Calls

Call 1

Inputs
(* x (+ 1/2 y))
(* x (+ 1/2 y))
(* x (+ 1/2 y))
(* x (+ 1/2 y))
(* x (+ 1/2 y))
(* x (+ 1/2 y))
(* x (+ 1/2 y))
(* x (+ 1/2 y))
(* -1 (* x (- (* -1 y) 1/2)))
(* -1 (* x (- (* -1 y) 1/2)))
(* -1 (* x (- (* -1 y) 1/2)))
(* -1 (* x (- (* -1 y) 1/2)))
(* 1/2 x)
(+ (* 1/2 x) (* x y))
(+ (* 1/2 x) (* x y))
(+ (* 1/2 x) (* x y))
(* x y)
(* y (+ x (* 1/2 (/ x y))))
(* y (+ x (* 1/2 (/ x y))))
(* y (+ x (* 1/2 (/ x y))))
(* x y)
(* -1 (* y (+ (* -1 x) (* -1/2 (/ x y)))))
(* -1 (* y (+ (* -1 x) (* -1/2 (/ x y)))))
(* -1 (* y (+ (* -1 x) (* -1/2 (/ x y)))))
z
(+ z (* x (+ 1/2 y)))
(+ z (* x (+ 1/2 y)))
(+ z (* x (+ 1/2 y)))
(* x (+ 1/2 y))
(* x (+ 1/2 (+ y (/ z x))))
(* x (+ 1/2 (+ y (/ z x))))
(* x (+ 1/2 (+ y (/ z x))))
(* -1 (* x (- (* -1 y) 1/2)))
(* -1 (* x (- (+ (* -1 y) (* -1 (/ z x))) 1/2)))
(* -1 (* x (- (+ (* -1 y) (* -1 (/ z x))) 1/2)))
(* -1 (* x (- (+ (* -1 y) (* -1 (/ z x))) 1/2)))
(+ z (* 1/2 x))
(+ z (+ (* 1/2 x) (* x y)))
(+ z (+ (* 1/2 x) (* x y)))
(+ z (+ (* 1/2 x) (* x y)))
(* x y)
(* y (+ x (+ (* 1/2 (/ x y)) (/ z y))))
(* y (+ x (+ (* 1/2 (/ x y)) (/ z y))))
(* y (+ x (+ (* 1/2 (/ x y)) (/ z y))))
(* x y)
(* -1 (* y (+ (* -1 x) (* -1 (/ (+ z (* 1/2 x)) y)))))
(* -1 (* y (+ (* -1 x) (* -1 (/ (+ z (* 1/2 x)) y)))))
(* -1 (* y (+ (* -1 x) (* -1 (/ (+ z (* 1/2 x)) y)))))
(+ (* 1/2 x) (* x y))
(+ z (+ (* 1/2 x) (* x y)))
(+ z (+ (* 1/2 x) (* x y)))
(+ z (+ (* 1/2 x) (* x y)))
z
(* z (+ 1 (+ (* 1/2 (/ x z)) (/ (* x y) z))))
(* z (+ 1 (+ (* 1/2 (/ x z)) (/ (* x y) z))))
(* z (+ 1 (+ (* 1/2 (/ x z)) (/ (* x y) z))))
z
(* -1 (* z (- (* -1 (/ (+ (* 1/2 x) (* x y)) z)) 1)))
(* -1 (* z (- (* -1 (/ (+ (* 1/2 x) (* x y)) z)) 1)))
(* -1 (* z (- (* -1 (/ (+ (* 1/2 x) (* x y)) z)) 1)))
(* 1/2 x)
(* 1/2 x)
(* 1/2 x)
(* 1/2 x)
(* 1/2 x)
(* 1/2 x)
(* 1/2 x)
(* 1/2 x)
(* 1/2 x)
(* 1/2 x)
(* 1/2 x)
(* 1/2 x)
(* x y)
(* x y)
(* x y)
(* x y)
(* x y)
(* x y)
(* x y)
(* x y)
(* x y)
(* x y)
(* x y)
(* x y)
(* x y)
(* x y)
(* x y)
(* x y)
(* x y)
(* x y)
(* x y)
(* x y)
(* x y)
(* x y)
(* x y)
(* x y)

Outputs
(* x (+ 1/2 y))
(*.f64 x (+.f64 #s(literal 1/2 binary64) y))
(* x (+ 1/2 y))
(*.f64 x (+.f64 #s(literal 1/2 binary64) y))
(* x (+ 1/2 y))
(*.f64 x (+.f64 #s(literal 1/2 binary64) y))
(* x (+ 1/2 y))
(*.f64 x (+.f64 #s(literal 1/2 binary64) y))
(* x (+ 1/2 y))
(*.f64 x (+.f64 #s(literal 1/2 binary64) y))
(* x (+ 1/2 y))
(*.f64 x (+.f64 #s(literal 1/2 binary64) y))
(* x (+ 1/2 y))
(*.f64 x (+.f64 #s(literal 1/2 binary64) y))
(* x (+ 1/2 y))
(*.f64 x (+.f64 #s(literal 1/2 binary64) y))
(* -1 (* x (- (* -1 y) 1/2)))
(*.f64 x (+.f64 #s(literal 1/2 binary64) y))
(* -1 (* x (- (* -1 y) 1/2)))
(*.f64 x (+.f64 #s(literal 1/2 binary64) y))
(* -1 (* x (- (* -1 y) 1/2)))
(*.f64 x (+.f64 #s(literal 1/2 binary64) y))
(* -1 (* x (- (* -1 y) 1/2)))
(*.f64 x (+.f64 #s(literal 1/2 binary64) y))
(* 1/2 x)
(*.f64 x #s(literal 1/2 binary64))
(+ (* 1/2 x) (* x y))
(*.f64 x (+.f64 #s(literal 1/2 binary64) y))
(+ (* 1/2 x) (* x y))
(*.f64 x (+.f64 #s(literal 1/2 binary64) y))
(+ (* 1/2 x) (* x y))
(*.f64 x (+.f64 #s(literal 1/2 binary64) y))
(* x y)
(*.f64 x y)
(* y (+ x (* 1/2 (/ x y))))
(*.f64 x (+.f64 #s(literal 1/2 binary64) y))
(* y (+ x (* 1/2 (/ x y))))
(*.f64 x (+.f64 #s(literal 1/2 binary64) y))
(* y (+ x (* 1/2 (/ x y))))
(*.f64 x (+.f64 #s(literal 1/2 binary64) y))
(* x y)
(*.f64 x y)
(* -1 (* y (+ (* -1 x) (* -1/2 (/ x y)))))
(*.f64 x (+.f64 #s(literal 1/2 binary64) y))
(* -1 (* y (+ (* -1 x) (* -1/2 (/ x y)))))
(*.f64 x (+.f64 #s(literal 1/2 binary64) y))
(* -1 (* y (+ (* -1 x) (* -1/2 (/ x y)))))
(*.f64 x (+.f64 #s(literal 1/2 binary64) y))
z
(+ z (* x (+ 1/2 y)))
(fma.f64 x (+.f64 #s(literal 1/2 binary64) y) z)
(+ z (* x (+ 1/2 y)))
(fma.f64 x (+.f64 #s(literal 1/2 binary64) y) z)
(+ z (* x (+ 1/2 y)))
(fma.f64 x (+.f64 #s(literal 1/2 binary64) y) z)
(* x (+ 1/2 y))
(*.f64 x (+.f64 #s(literal 1/2 binary64) y))
(* x (+ 1/2 (+ y (/ z x))))
(fma.f64 x (+.f64 #s(literal 1/2 binary64) y) z)
(* x (+ 1/2 (+ y (/ z x))))
(fma.f64 x (+.f64 #s(literal 1/2 binary64) y) z)
(* x (+ 1/2 (+ y (/ z x))))
(fma.f64 x (+.f64 #s(literal 1/2 binary64) y) z)
(* -1 (* x (- (* -1 y) 1/2)))
(*.f64 x (+.f64 #s(literal 1/2 binary64) y))
(* -1 (* x (- (+ (* -1 y) (* -1 (/ z x))) 1/2)))
(fma.f64 x (+.f64 #s(literal 1/2 binary64) y) z)
(* -1 (* x (- (+ (* -1 y) (* -1 (/ z x))) 1/2)))
(fma.f64 x (+.f64 #s(literal 1/2 binary64) y) z)
(* -1 (* x (- (+ (* -1 y) (* -1 (/ z x))) 1/2)))
(fma.f64 x (+.f64 #s(literal 1/2 binary64) y) z)
(+ z (* 1/2 x))
(fma.f64 x #s(literal 1/2 binary64) z)
(+ z (+ (* 1/2 x) (* x y)))
(fma.f64 x (+.f64 #s(literal 1/2 binary64) y) z)
(+ z (+ (* 1/2 x) (* x y)))
(fma.f64 x (+.f64 #s(literal 1/2 binary64) y) z)
(+ z (+ (* 1/2 x) (* x y)))
(fma.f64 x (+.f64 #s(literal 1/2 binary64) y) z)
(* x y)
(*.f64 x y)
(* y (+ x (+ (* 1/2 (/ x y)) (/ z y))))
(fma.f64 x (+.f64 #s(literal 1/2 binary64) y) z)
(* y (+ x (+ (* 1/2 (/ x y)) (/ z y))))
(fma.f64 x (+.f64 #s(literal 1/2 binary64) y) z)
(* y (+ x (+ (* 1/2 (/ x y)) (/ z y))))
(fma.f64 x (+.f64 #s(literal 1/2 binary64) y) z)
(* x y)
(*.f64 x y)
(* -1 (* y (+ (* -1 x) (* -1 (/ (+ z (* 1/2 x)) y)))))
(fma.f64 x (+.f64 #s(literal 1/2 binary64) y) z)
(* -1 (* y (+ (* -1 x) (* -1 (/ (+ z (* 1/2 x)) y)))))
(fma.f64 x (+.f64 #s(literal 1/2 binary64) y) z)
(* -1 (* y (+ (* -1 x) (* -1 (/ (+ z (* 1/2 x)) y)))))
(fma.f64 x (+.f64 #s(literal 1/2 binary64) y) z)
(+ (* 1/2 x) (* x y))
(*.f64 x (+.f64 #s(literal 1/2 binary64) y))
(+ z (+ (* 1/2 x) (* x y)))
(fma.f64 x (+.f64 #s(literal 1/2 binary64) y) z)
(+ z (+ (* 1/2 x) (* x y)))
(fma.f64 x (+.f64 #s(literal 1/2 binary64) y) z)
(+ z (+ (* 1/2 x) (* x y)))
(fma.f64 x (+.f64 #s(literal 1/2 binary64) y) z)
z
(* z (+ 1 (+ (* 1/2 (/ x z)) (/ (* x y) z))))
(fma.f64 x (+.f64 #s(literal 1/2 binary64) y) z)
(* z (+ 1 (+ (* 1/2 (/ x z)) (/ (* x y) z))))
(fma.f64 x (+.f64 #s(literal 1/2 binary64) y) z)
(* z (+ 1 (+ (* 1/2 (/ x z)) (/ (* x y) z))))
(fma.f64 x (+.f64 #s(literal 1/2 binary64) y) z)
z
(* -1 (* z (- (* -1 (/ (+ (* 1/2 x) (* x y)) z)) 1)))
(fma.f64 x (+.f64 #s(literal 1/2 binary64) y) z)
(* -1 (* z (- (* -1 (/ (+ (* 1/2 x) (* x y)) z)) 1)))
(fma.f64 x (+.f64 #s(literal 1/2 binary64) y) z)
(* -1 (* z (- (* -1 (/ (+ (* 1/2 x) (* x y)) z)) 1)))
(fma.f64 x (+.f64 #s(literal 1/2 binary64) y) z)
(* 1/2 x)
(*.f64 x #s(literal 1/2 binary64))
(* 1/2 x)
(*.f64 x #s(literal 1/2 binary64))
(* 1/2 x)
(*.f64 x #s(literal 1/2 binary64))
(* 1/2 x)
(*.f64 x #s(literal 1/2 binary64))
(* 1/2 x)
(*.f64 x #s(literal 1/2 binary64))
(* 1/2 x)
(*.f64 x #s(literal 1/2 binary64))
(* 1/2 x)
(*.f64 x #s(literal 1/2 binary64))
(* 1/2 x)
(*.f64 x #s(literal 1/2 binary64))
(* 1/2 x)
(*.f64 x #s(literal 1/2 binary64))
(* 1/2 x)
(*.f64 x #s(literal 1/2 binary64))
(* 1/2 x)
(*.f64 x #s(literal 1/2 binary64))
(* 1/2 x)
(*.f64 x #s(literal 1/2 binary64))
(* x y)
(*.f64 x y)
(* x y)
(*.f64 x y)
(* x y)
(*.f64 x y)
(* x y)
(*.f64 x y)
(* x y)
(*.f64 x y)
(* x y)
(*.f64 x y)
(* x y)
(*.f64 x y)
(* x y)
(*.f64 x y)
(* x y)
(*.f64 x y)
(* x y)
(*.f64 x y)
(* x y)
(*.f64 x y)
(* x y)
(*.f64 x y)
(* x y)
(*.f64 x y)
(* x y)
(*.f64 x y)
(* x y)
(*.f64 x y)
(* x y)
(*.f64 x y)
(* x y)
(*.f64 x y)
(* x y)
(*.f64 x y)
(* x y)
(*.f64 x y)
(* x y)
(*.f64 x y)
(* x y)
(*.f64 x y)
(* x y)
(*.f64 x y)
(* x y)
(*.f64 x y)
(* x y)
(*.f64 x y)

eval38.0ms (0.6%)

Memory: -0.4MiB live, 74.5MiB allocated
Compiler: Compiled 7 790 to 739 computations (90.5% saved)

prune37.0ms (0.6%)

Memory

12.5MiB live, 96.5MiB allocated

Pruning

5 alts after pruning (5 fresh and 0 done)

	Pruned	Kept	Total
New	330	5	335
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	331	5	336

Accuracy

100.0%

Counts

336 → 5

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	100.0%	(fma.f64 (+.f64 y #s(literal 1/2 binary64)) x z)
▶	61.3%	(fma.f64 x #s(literal 1/2 binary64) z)
▶	78.0%	(+.f64 (*.f64 x y) z)
▶	61.4%	(*.f64 x (+.f64 #s(literal 1/2 binary64) y))
▶	39.8%	(*.f64 x y)

Compiler

Compiled 76 to 52 computations (31.6% saved)

simplify6.0ms (0.1%)

Memory

16.6MiB live, 16.6MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 8 expressions of interest:

New	Metric	Score	Program
✓	cost-diff	0	(*.f64 x y)
✓	cost-diff	128	(+.f64 (*.f64 x y) z)
✓	cost-diff	0	(+.f64 #s(literal 1/2 binary64) y)
✓	cost-diff	0	(*.f64 x (+.f64 #s(literal 1/2 binary64) y))
✓	cost-diff	0	(fma.f64 x #s(literal 1/2 binary64) z)
✓	cost-diff	0	(*.f64 x y)
✓	cost-diff	0	(+.f64 y #s(literal 1/2 binary64))
✓	cost-diff	0	(fma.f64 (+.f64 y #s(literal 1/2 binary64)) x z)

Rules

28×	`lower-fma.f32`
28×	`lower-+.f32`
24×	`lower-fma.f64`
22×	`lower-+.f64`
12×	`lower-*.f32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	11	47
0	20	47
1	29	47
2	32	47
3	34	47
0	34	46

Stop Event

1×	iter limit
1×	saturated
1×	iter limit

Calls

Call 1

Inputs
(fma.f64 (+.f64 y #s(literal 1/2 binary64)) x z)
(+.f64 y #s(literal 1/2 binary64))
y
#s(literal 1/2 binary64)
x
z
(*.f64 x y)
x
y
(fma.f64 x #s(literal 1/2 binary64) z)
x
#s(literal 1/2 binary64)
z
(*.f64 x (+.f64 #s(literal 1/2 binary64) y))
x
(+.f64 #s(literal 1/2 binary64) y)
#s(literal 1/2 binary64)
y
(+.f64 (*.f64 x y) z)
(*.f64 x y)
x
y
z

Outputs
(fma.f64 (+.f64 y #s(literal 1/2 binary64)) x z)
(fma.f64 x (+.f64 y #s(literal 1/2 binary64)) z)
(+.f64 y #s(literal 1/2 binary64))
y
#s(literal 1/2 binary64)
x
z
(*.f64 x y)
(*.f64 y x)
x
y
(fma.f64 x #s(literal 1/2 binary64) z)
(fma.f64 #s(literal 1/2 binary64) x z)
x
#s(literal 1/2 binary64)
z
(*.f64 x (+.f64 #s(literal 1/2 binary64) y))
(*.f64 x (+.f64 y #s(literal 1/2 binary64)))
x
(+.f64 #s(literal 1/2 binary64) y)
(+.f64 y #s(literal 1/2 binary64))
#s(literal 1/2 binary64)
y
(+.f64 (*.f64 x y) z)
(fma.f64 y x z)
(*.f64 x y)
(*.f64 y x)
x
y
z

localize41.0ms (0.7%)

Memory

-21.0MiB live, 99.4MiB allocated

Localize:

Found 8 expressions of interest:

New	Metric	Score	Program
✓	accuracy	100.0%	(*.f64 x y)
✓	accuracy	100.0%	(+.f64 (*.f64 x y) z)
✓	accuracy	100.0%	(+.f64 #s(literal 1/2 binary64) y)
✓	accuracy	100.0%	(*.f64 x (+.f64 #s(literal 1/2 binary64) y))
✓	accuracy	100.0%	(fma.f64 x #s(literal 1/2 binary64) z)
✓	accuracy	100.0%	(*.f64 x y)
✓	accuracy	100.0%	(fma.f64 (+.f64 y #s(literal 1/2 binary64)) x z)
✓	accuracy	100.0%	(+.f64 y #s(literal 1/2 binary64))

Samples

26.0ms

256×

valid

Compiler

Compiled 51 to 15 computations (70.6% saved)

Precisions

Click to see histograms. Total time spent on operations: 12.0ms

ival-add: 6.0ms (48.9% of total)

ival-mult: 6.0ms (48.9% of total)

ival-true: 0.0ms (0% of total)

exact: 0.0ms (0% of total)

ival-assert: 0.0ms (0% of total)

series5.0ms (0.1%)

Memory

10.4MiB live, 10.4MiB allocated

Counts

7 → 168

Calls

Call 1

Inputs
#<alt (fma.f64 (+.f64 y #s(literal 1/2 binary64)) x z)>
#<alt (+.f64 y #s(literal 1/2 binary64))>
#<alt (*.f64 x y)>
#<alt (fma.f64 x #s(literal 1/2 binary64) z)>
#<alt (*.f64 x (+.f64 #s(literal 1/2 binary64) y))>
#<alt (+.f64 #s(literal 1/2 binary64) y)>
#<alt (+.f64 (*.f64 x y) z)>

Outputs
#<alt (+ z (* 1/2 x))>
#<alt (+ z (+ (* 1/2 x) (* x y)))>
#<alt (+ z (+ (* 1/2 x) (* x y)))>
#<alt (+ z (+ (* 1/2 x) (* x y)))>
#<alt (* x y)>
#<alt (* y (+ x (+ (* 1/2 (/ x y)) (/ z y))))>
#<alt (* y (+ x (+ (* 1/2 (/ x y)) (/ z y))))>
#<alt (* y (+ x (+ (* 1/2 (/ x y)) (/ z y))))>
#<alt (* x y)>
#<alt (* -1 (* y (+ (* -1 x) (* -1 (/ (+ z (* 1/2 x)) y)))))>
#<alt (* -1 (* y (+ (* -1 x) (* -1 (/ (+ z (* 1/2 x)) y)))))>
#<alt (* -1 (* y (+ (* -1 x) (* -1 (/ (+ z (* 1/2 x)) y)))))>
#<alt z>
#<alt (+ z (* x (+ 1/2 y)))>
#<alt (+ z (* x (+ 1/2 y)))>
#<alt (+ z (* x (+ 1/2 y)))>
#<alt (* x (+ 1/2 y))>
#<alt (* x (+ 1/2 (+ y (/ z x))))>
#<alt (* x (+ 1/2 (+ y (/ z x))))>
#<alt (* x (+ 1/2 (+ y (/ z x))))>
#<alt (* x (+ 1/2 y))>
#<alt (* -1 (* x (+ (* -1 (+ 1/2 y)) (* -1 (/ z x)))))>
#<alt (* -1 (* x (+ (* -1 (+ 1/2 y)) (* -1 (/ z x)))))>
#<alt (* -1 (* x (+ (* -1 (+ 1/2 y)) (* -1 (/ z x)))))>
#<alt (* x (+ 1/2 y))>
#<alt (+ z (* x (+ 1/2 y)))>
#<alt (+ z (* x (+ 1/2 y)))>
#<alt (+ z (* x (+ 1/2 y)))>
#<alt z>
#<alt (* z (+ 1 (/ (* x (+ 1/2 y)) z)))>
#<alt (* z (+ 1 (/ (* x (+ 1/2 y)) z)))>
#<alt (* z (+ 1 (/ (* x (+ 1/2 y)) z)))>
#<alt z>
#<alt (* -1 (* z (- (* -1 (/ (* x (+ 1/2 y)) z)) 1)))>
#<alt (* -1 (* z (- (* -1 (/ (* x (+ 1/2 y)) z)) 1)))>
#<alt (* -1 (* z (- (* -1 (/ (* x (+ 1/2 y)) z)) 1)))>
#<alt 1/2>
#<alt (+ 1/2 y)>
#<alt (+ 1/2 y)>
#<alt (+ 1/2 y)>
#<alt y>
#<alt (* y (+ 1 (* 1/2 (/ 1 y))))>
#<alt (* y (+ 1 (* 1/2 (/ 1 y))))>
#<alt (* y (+ 1 (* 1/2 (/ 1 y))))>
#<alt y>
#<alt (* y (+ 1 (* 1/2 (/ 1 y))))>
#<alt (* y (+ 1 (* 1/2 (/ 1 y))))>
#<alt (* y (+ 1 (* 1/2 (/ 1 y))))>
#<alt (* x y)>
#<alt (* x y)>
#<alt (* x y)>
#<alt (* x y)>
#<alt (* x y)>
#<alt (* x y)>
#<alt (* x y)>
#<alt (* x y)>
#<alt (* x y)>
#<alt (* x y)>
#<alt (* x y)>
#<alt (* x y)>
#<alt (* x y)>
#<alt (* x y)>
#<alt (* x y)>
#<alt (* x y)>
#<alt (* x y)>
#<alt (* x y)>
#<alt (* x y)>
#<alt (* x y)>
#<alt (* x y)>
#<alt (* x y)>
#<alt (* x y)>
#<alt (* x y)>
#<alt z>
#<alt (+ z (* 1/2 x))>
#<alt (+ z (* 1/2 x))>
#<alt (+ z (* 1/2 x))>
#<alt (* 1/2 x)>
#<alt (* x (+ 1/2 (/ z x)))>
#<alt (* x (+ 1/2 (/ z x)))>
#<alt (* x (+ 1/2 (/ z x)))>
#<alt (* 1/2 x)>
#<alt (* -1 (* x (- (* -1 (/ z x)) 1/2)))>
#<alt (* -1 (* x (- (* -1 (/ z x)) 1/2)))>
#<alt (* -1 (* x (- (* -1 (/ z x)) 1/2)))>
#<alt (* 1/2 x)>
#<alt (+ z (* 1/2 x))>
#<alt (+ z (* 1/2 x))>
#<alt (+ z (* 1/2 x))>
#<alt z>
#<alt (* z (+ 1 (* 1/2 (/ x z))))>
#<alt (* z (+ 1 (* 1/2 (/ x z))))>
#<alt (* z (+ 1 (* 1/2 (/ x z))))>
#<alt z>
#<alt (* -1 (* z (- (* -1/2 (/ x z)) 1)))>
#<alt (* -1 (* z (- (* -1/2 (/ x z)) 1)))>
#<alt (* -1 (* z (- (* -1/2 (/ x z)) 1)))>
#<alt (* x (+ 1/2 y))>
#<alt (* x (+ 1/2 y))>
#<alt (* x (+ 1/2 y))>
#<alt (* x (+ 1/2 y))>
#<alt (* x (+ 1/2 y))>
#<alt (* x (+ 1/2 y))>
#<alt (* x (+ 1/2 y))>
#<alt (* x (+ 1/2 y))>
#<alt (* x (+ 1/2 y))>
#<alt (* x (+ 1/2 y))>
#<alt (* x (+ 1/2 y))>
#<alt (* x (+ 1/2 y))>
#<alt (* 1/2 x)>
#<alt (+ (* 1/2 x) (* x y))>
#<alt (+ (* 1/2 x) (* x y))>
#<alt (+ (* 1/2 x) (* x y))>
#<alt (* x y)>
#<alt (* y (+ x (* 1/2 (/ x y))))>
#<alt (* y (+ x (* 1/2 (/ x y))))>
#<alt (* y (+ x (* 1/2 (/ x y))))>
#<alt (* x y)>
#<alt (* -1 (* y (+ (* -1 x) (* -1/2 (/ x y)))))>
#<alt (* -1 (* y (+ (* -1 x) (* -1/2 (/ x y)))))>
#<alt (* -1 (* y (+ (* -1 x) (* -1/2 (/ x y)))))>
#<alt 1/2>
#<alt (+ 1/2 y)>
#<alt (+ 1/2 y)>
#<alt (+ 1/2 y)>
#<alt y>
#<alt (* y (+ 1 (* 1/2 (/ 1 y))))>
#<alt (* y (+ 1 (* 1/2 (/ 1 y))))>
#<alt (* y (+ 1 (* 1/2 (/ 1 y))))>
#<alt y>
#<alt (* y (+ 1 (* 1/2 (/ 1 y))))>
#<alt (* y (+ 1 (* 1/2 (/ 1 y))))>
#<alt (* y (+ 1 (* 1/2 (/ 1 y))))>
#<alt z>
#<alt (+ z (* x y))>
#<alt (+ z (* x y))>
#<alt (+ z (* x y))>
#<alt (* x y)>
#<alt (* x (+ y (/ z x)))>
#<alt (* x (+ y (/ z x)))>
#<alt (* x (+ y (/ z x)))>
#<alt (* x y)>
#<alt (* -1 (* x (+ (* -1 y) (* -1 (/ z x)))))>
#<alt (* -1 (* x (+ (* -1 y) (* -1 (/ z x)))))>
#<alt (* -1 (* x (+ (* -1 y) (* -1 (/ z x)))))>
#<alt z>
#<alt (+ z (* x y))>
#<alt (+ z (* x y))>
#<alt (+ z (* x y))>
#<alt (* x y)>
#<alt (* y (+ x (/ z y)))>
#<alt (* y (+ x (/ z y)))>
#<alt (* y (+ x (/ z y)))>
#<alt (* x y)>
#<alt (* -1 (* y (+ (* -1 x) (* -1 (/ z y)))))>
#<alt (* -1 (* y (+ (* -1 x) (* -1 (/ z y)))))>
#<alt (* -1 (* y (+ (* -1 x) (* -1 (/ z y)))))>
#<alt (* x y)>
#<alt (+ z (* x y))>
#<alt (+ z (* x y))>
#<alt (+ z (* x y))>
#<alt z>
#<alt (* z (+ 1 (/ (* x y) z)))>
#<alt (* z (+ 1 (/ (* x y) z)))>
#<alt (* z (+ 1 (/ (* x y) z)))>
#<alt z>
#<alt (* -1 (* z (- (* -1 (/ (* x y) z)) 1)))>
#<alt (* -1 (* z (- (* -1 (/ (* x y) z)) 1)))>
#<alt (* -1 (* z (- (* -1 (/ (* x y) z)) 1)))>

Calls

42 calls:

Time	Variable		Point	Expression
0.0ms	x	@	-inf	(+ (* (+ y 1/2) x) z)
0.0ms	y	@	inf	(+ (* (+ y 1/2) x) z)
0.0ms	y	@	0	(+ (* (+ y 1/2) x) z)
0.0ms	y	@	-inf	(+ (* (+ y 1/2) x) z)
0.0ms	x	@	0	(+ (* (+ y 1/2) x) z)

rewrite547.0ms (9.1%)

Memory

-0.9MiB live, 349.7MiB allocated

Algorithm

1×	batch-egg-rewrite

Rules

8 308×	`lower-fma.f32`
8 304×	`lower-fma.f64`
4 880×	`lower-*.f32`
4 876×	`lower-*.f64`
3 342×	`lower-/.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	11	29
0	20	29
1	84	29
2	630	29
3	7950	29
0	8328	28

Stop Event

1×	iter limit
1×	node limit
1×	iter limit

Counts

7 → 478

Calls

Call 1

Inputs
(fma.f64 (+.f64 y #s(literal 1/2 binary64)) x z)
(+.f64 y #s(literal 1/2 binary64))
(*.f64 x y)
(fma.f64 x #s(literal 1/2 binary64) z)
(*.f64 x (+.f64 #s(literal 1/2 binary64) y))
(+.f64 #s(literal 1/2 binary64) y)
(+.f64 (*.f64 x y) z)

Outputs
(+.f64 z (*.f64 x (+.f64 y #s(literal 1/2 binary64))))
(+.f64 (*.f64 y x) (fma.f64 #s(literal 1/2 binary64) x z))
(+.f64 (fma.f64 #s(literal 1/2 binary64) x z) (*.f64 y x))
(+.f64 (fma.f64 y x z) (*.f64 #s(literal 1/2 binary64) x))
(+.f64 (*.f64 x (+.f64 y #s(literal 1/2 binary64))) z)
(+.f64 (*.f64 #s(literal 1/2 binary64) x) (fma.f64 y x z))
(+.f64 (/.f64 (.f64 (+.f64 y #s(literal 1/2 binary64)) (.f64 (+.f64 y #s(literal 1/2 binary64)) (.f64 x x))) (fma.f64 x (+.f64 y #s(literal 1/2 binary64)) (neg.f64 z))) (neg.f64 (/.f64 (.f64 z z) (fma.f64 x (+.f64 y #s(literal 1/2 binary64)) (neg.f64 z)))))
(-.f64 (/.f64 (.f64 (+.f64 y #s(literal 1/2 binary64)) (.f64 (+.f64 y #s(literal 1/2 binary64)) (.f64 x x))) (fma.f64 x (+.f64 y #s(literal 1/2 binary64)) (neg.f64 z))) (/.f64 (.f64 z z) (fma.f64 x (+.f64 y #s(literal 1/2 binary64)) (neg.f64 z))))
(-.f64 (/.f64 (.f64 x (.f64 x #s(literal 1/4 binary64))) (-.f64 (.f64 #s(literal 1/2 binary64) x) z)) (-.f64 (/.f64 (.f64 z z) (-.f64 (.f64 #s(literal 1/2 binary64) x) z)) (.f64 y x)))
(-.f64 (/.f64 (.f64 z z) (-.f64 z (.f64 x (+.f64 y #s(literal 1/2 binary64))))) (/.f64 (.f64 (+.f64 y #s(literal 1/2 binary64)) (.f64 (+.f64 y #s(literal 1/2 binary64)) (.f64 x x))) (-.f64 z (.f64 x (+.f64 y #s(literal 1/2 binary64))))))
(-.f64 (fma.f64 #s(literal 1/2 binary64) x (/.f64 (.f64 y (.f64 x (.f64 y x))) (-.f64 (.f64 y x) z))) (/.f64 (.f64 z z) (-.f64 (.f64 y x) z)))
(fma.f64 y x (fma.f64 #s(literal 1/2 binary64) x z))
(fma.f64 #s(literal 1/2 binary64) x (fma.f64 y x z))
(fma.f64 x y (fma.f64 #s(literal 1/2 binary64) x z))
(fma.f64 x #s(literal 1/2 binary64) (fma.f64 y x z))
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(/.f64 (.f64 (.f64 (.f64 (fma.f64 y x z) (fma.f64 (.f64 y x) (-.f64 (.f64 y x) z) (.f64 z z))) (fma.f64 y (.f64 x (.f64 y (.f64 x (.f64 y x)))) (.f64 (.f64 z (neg.f64 z)) z))) (/.f64 #s(literal 1 binary64) (-.f64 (.f64 y x) z))) (fma.f64 (.f64 z z) (fma.f64 y (.f64 x (.f64 y x)) (.f64 z z)) (.f64 (.f64 y (.f64 x (.f64 y x))) (.f64 y (.f64 x (.f64 y x))))))
(/.f64 (.f64 (.f64 (fma.f64 y (.f64 x (.f64 y x)) (.f64 z z)) (.f64 (fma.f64 y x z) (-.f64 (.f64 y x) z))) (/.f64 #s(literal 1 binary64) (-.f64 (.f64 y x) z))) (fma.f64 y (.f64 x (.f64 y x)) (*.f64 z z)))
(pow.f64 (/.f64 #s(literal 1 binary64) (fma.f64 y x z)) #s(literal -1 binary64))
(.f64 (fma.f64 y x z) (.f64 (-.f64 (.f64 y x) z) (/.f64 #s(literal 1 binary64) (-.f64 (.f64 y x) z))))
(.f64 (fma.f64 y x z) (/.f64 (-.f64 (.f64 y x) z) (-.f64 (*.f64 y x) z)))
(.f64 (.f64 (fma.f64 y x z) (fma.f64 (.f64 y x) (-.f64 (.f64 y x) z) (.f64 z z))) (/.f64 #s(literal 1 binary64) (fma.f64 (.f64 y x) (-.f64 (.f64 y x) z) (.f64 z z))))
(.f64 (fma.f64 (.f64 y x) (-.f64 (.f64 y x) z) (.f64 z z)) (.f64 (fma.f64 y x z) (/.f64 #s(literal 1 binary64) (fma.f64 (.f64 y x) (-.f64 (.f64 y x) z) (.f64 z z)))))
(.f64 (fma.f64 (.f64 y x) (-.f64 (.f64 y x) z) (.f64 z z)) (/.f64 (fma.f64 y x z) (fma.f64 (.f64 y x) (-.f64 (.f64 y x) z) (*.f64 z z))))
(.f64 (.f64 (fma.f64 y x z) (-.f64 (.f64 y x) z)) (/.f64 #s(literal 1 binary64) (-.f64 (.f64 y x) z)))
(.f64 (.f64 (fma.f64 (.f64 y x) (-.f64 (.f64 y x) z) (.f64 z z)) (neg.f64 (fma.f64 y x z))) (/.f64 #s(literal 1 binary64) (neg.f64 (fma.f64 (.f64 y x) (-.f64 (.f64 y x) z) (.f64 z z)))))
(.f64 (neg.f64 (.f64 (fma.f64 y x z) (-.f64 (.f64 y x) z))) (/.f64 #s(literal 1 binary64) (neg.f64 (-.f64 (.f64 y x) z))))
(*.f64 #s(literal 1 binary64) (fma.f64 y x z))
(.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (.f64 y x) (-.f64 (.f64 y x) z) (.f64 z z))) (.f64 (fma.f64 y x z) (fma.f64 (.f64 y x) (-.f64 (.f64 y x) z) (.f64 z z))))
(.f64 (/.f64 #s(literal 1 binary64) (-.f64 (.f64 y x) z)) (.f64 (fma.f64 y x z) (-.f64 (.f64 y x) z)))
(.f64 (.f64 (fma.f64 y x z) (-.f64 z (.f64 y x))) (/.f64 #s(literal 1 binary64) (-.f64 z (.f64 y x))))
(.f64 (/.f64 (.f64 (fma.f64 y x z) (-.f64 (.f64 y x) z)) (.f64 (fma.f64 y x z) (-.f64 (*.f64 y x) z))) (fma.f64 y x z))
(.f64 (/.f64 (.f64 (fma.f64 y x z) (fma.f64 (.f64 y x) (-.f64 (.f64 y x) z) (.f64 z z))) (fma.f64 (.f64 z (-.f64 z (.f64 y x))) (.f64 z (.f64 (-.f64 z (.f64 y x)) (.f64 z (-.f64 z (.f64 y x))))) (.f64 (.f64 y x) (.f64 (.f64 y (.f64 x (.f64 y x))) (.f64 y (.f64 x (.f64 y (.f64 x (.f64 y x))))))))) (fma.f64 (.f64 z (-.f64 z (.f64 y x))) (-.f64 (.f64 z (-.f64 z (.f64 y x))) (.f64 y (.f64 x (.f64 y x)))) (.f64 (.f64 y (.f64 x (.f64 y x))) (.f64 y (.f64 x (*.f64 y x))))))
(.f64 (/.f64 (.f64 (fma.f64 y x z) (fma.f64 (.f64 y x) (-.f64 (.f64 y x) z) (.f64 z z))) (.f64 (fma.f64 (.f64 y x) (-.f64 (.f64 y x) z) (.f64 z z)) (fma.f64 (fma.f64 y x z) (-.f64 (.f64 y x) z) (.f64 z (.f64 y x))))) (fma.f64 (fma.f64 y x z) (-.f64 (.f64 y x) z) (.f64 z (*.f64 y x))))
(.f64 (/.f64 (.f64 (fma.f64 y x z) (-.f64 (.f64 y x) z)) (fma.f64 y (.f64 x (.f64 y (.f64 x (.f64 y x)))) (.f64 (.f64 z (neg.f64 z)) z))) (fma.f64 y (.f64 x (.f64 y x)) (.f64 z (fma.f64 y x z))))

simplify328.0ms (5.5%)

Memory

27.6MiB live, 253.3MiB allocated

Algorithm

1×	egg-herbie

Rules

8 198×	`lower-fma.f64`
8 198×	`lower-fma.f32`
3 622×	`lower-*.f64`
3 622×	`lower-*.f32`
1 284×	`div-sub`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	85	720
1	290	720
2	795	720
3	2300	720
4	4011	720
5	6468	720
0	8258	647

Stop Event

1×	iter limit
1×	node limit

Counts

168 → 154

Calls

Call 1

Inputs
(+ z (* 1/2 x))
(+ z (+ (* 1/2 x) (* x y)))
(+ z (+ (* 1/2 x) (* x y)))
(+ z (+ (* 1/2 x) (* x y)))
(* x y)
(* y (+ x (+ (* 1/2 (/ x y)) (/ z y))))
(* y (+ x (+ (* 1/2 (/ x y)) (/ z y))))
(* y (+ x (+ (* 1/2 (/ x y)) (/ z y))))
(* x y)
(* -1 (* y (+ (* -1 x) (* -1 (/ (+ z (* 1/2 x)) y)))))
(* -1 (* y (+ (* -1 x) (* -1 (/ (+ z (* 1/2 x)) y)))))
(* -1 (* y (+ (* -1 x) (* -1 (/ (+ z (* 1/2 x)) y)))))
z
(+ z (* x (+ 1/2 y)))
(+ z (* x (+ 1/2 y)))
(+ z (* x (+ 1/2 y)))
(* x (+ 1/2 y))
(* x (+ 1/2 (+ y (/ z x))))
(* x (+ 1/2 (+ y (/ z x))))
(* x (+ 1/2 (+ y (/ z x))))
(* x (+ 1/2 y))
(* -1 (* x (+ (* -1 (+ 1/2 y)) (* -1 (/ z x)))))
(* -1 (* x (+ (* -1 (+ 1/2 y)) (* -1 (/ z x)))))
(* -1 (* x (+ (* -1 (+ 1/2 y)) (* -1 (/ z x)))))
(* x (+ 1/2 y))
(+ z (* x (+ 1/2 y)))
(+ z (* x (+ 1/2 y)))
(+ z (* x (+ 1/2 y)))
z
(* z (+ 1 (/ (* x (+ 1/2 y)) z)))
(* z (+ 1 (/ (* x (+ 1/2 y)) z)))
(* z (+ 1 (/ (* x (+ 1/2 y)) z)))
z
(* -1 (* z (- (* -1 (/ (* x (+ 1/2 y)) z)) 1)))
(* -1 (* z (- (* -1 (/ (* x (+ 1/2 y)) z)) 1)))
(* -1 (* z (- (* -1 (/ (* x (+ 1/2 y)) z)) 1)))
1/2
(+ 1/2 y)
(+ 1/2 y)
(+ 1/2 y)
y
(* y (+ 1 (* 1/2 (/ 1 y))))
(* y (+ 1 (* 1/2 (/ 1 y))))
(* y (+ 1 (* 1/2 (/ 1 y))))
y
(* y (+ 1 (* 1/2 (/ 1 y))))
(* y (+ 1 (* 1/2 (/ 1 y))))
(* y (+ 1 (* 1/2 (/ 1 y))))
(* x y)
(* x y)
(* x y)
(* x y)
(* x y)
(* x y)
(* x y)
(* x y)
(* x y)
(* x y)
(* x y)
(* x y)
(* x y)
(* x y)
(* x y)
(* x y)
(* x y)
(* x y)
(* x y)
(* x y)
(* x y)
(* x y)
(* x y)
(* x y)
z
(+ z (* 1/2 x))
(+ z (* 1/2 x))
(+ z (* 1/2 x))
(* 1/2 x)
(* x (+ 1/2 (/ z x)))
(* x (+ 1/2 (/ z x)))
(* x (+ 1/2 (/ z x)))
(* 1/2 x)
(* -1 (* x (- (* -1 (/ z x)) 1/2)))
(* -1 (* x (- (* -1 (/ z x)) 1/2)))
(* -1 (* x (- (* -1 (/ z x)) 1/2)))
(* 1/2 x)
(+ z (* 1/2 x))
(+ z (* 1/2 x))
(+ z (* 1/2 x))
z
(* z (+ 1 (* 1/2 (/ x z))))
(* z (+ 1 (* 1/2 (/ x z))))
(* z (+ 1 (* 1/2 (/ x z))))
z
(* -1 (* z (- (* -1/2 (/ x z)) 1)))
(* -1 (* z (- (* -1/2 (/ x z)) 1)))
(* -1 (* z (- (* -1/2 (/ x z)) 1)))
(* x (+ 1/2 y))
(* x (+ 1/2 y))
(* x (+ 1/2 y))
(* x (+ 1/2 y))
(* x (+ 1/2 y))
(* x (+ 1/2 y))
(* x (+ 1/2 y))
(* x (+ 1/2 y))
(* x (+ 1/2 y))
(* x (+ 1/2 y))
(* x (+ 1/2 y))
(* x (+ 1/2 y))
(* 1/2 x)
(+ (* 1/2 x) (* x y))
(+ (* 1/2 x) (* x y))
(+ (* 1/2 x) (* x y))
(* x y)
(* y (+ x (* 1/2 (/ x y))))
(* y (+ x (* 1/2 (/ x y))))
(* y (+ x (* 1/2 (/ x y))))
(* x y)
(* -1 (* y (+ (* -1 x) (* -1/2 (/ x y)))))
(* -1 (* y (+ (* -1 x) (* -1/2 (/ x y)))))
(* -1 (* y (+ (* -1 x) (* -1/2 (/ x y)))))
1/2
(+ 1/2 y)
(+ 1/2 y)
(+ 1/2 y)
y
(* y (+ 1 (* 1/2 (/ 1 y))))
(* y (+ 1 (* 1/2 (/ 1 y))))
(* y (+ 1 (* 1/2 (/ 1 y))))
y
(* y (+ 1 (* 1/2 (/ 1 y))))
(* y (+ 1 (* 1/2 (/ 1 y))))
(* y (+ 1 (* 1/2 (/ 1 y))))
z
(+ z (* x y))
(+ z (* x y))
(+ z (* x y))
(* x y)
(* x (+ y (/ z x)))
(* x (+ y (/ z x)))
(* x (+ y (/ z x)))
(* x y)
(* -1 (* x (+ (* -1 y) (* -1 (/ z x)))))
(* -1 (* x (+ (* -1 y) (* -1 (/ z x)))))
(* -1 (* x (+ (* -1 y) (* -1 (/ z x)))))
z
(+ z (* x y))
(+ z (* x y))
(+ z (* x y))
(* x y)
(* y (+ x (/ z y)))
(* y (+ x (/ z y)))
(* y (+ x (/ z y)))
(* x y)
(* -1 (* y (+ (* -1 x) (* -1 (/ z y)))))
(* -1 (* y (+ (* -1 x) (* -1 (/ z y)))))
(* -1 (* y (+ (* -1 x) (* -1 (/ z y)))))
(* x y)
(+ z (* x y))
(+ z (* x y))
(+ z (* x y))
z
(* z (+ 1 (/ (* x y) z)))
(* z (+ 1 (/ (* x y) z)))
(* z (+ 1 (/ (* x y) z)))
z
(* -1 (* z (- (* -1 (/ (* x y) z)) 1)))
(* -1 (* z (- (* -1 (/ (* x y) z)) 1)))
(* -1 (* z (- (* -1 (/ (* x y) z)) 1)))

Outputs
(+ z (* 1/2 x))
(fma.f64 #s(literal 1/2 binary64) x z)
(+ z (+ (* 1/2 x) (* x y)))
(fma.f64 x (+.f64 #s(literal 1/2 binary64) y) z)
(+ z (+ (* 1/2 x) (* x y)))
(fma.f64 x (+.f64 #s(literal 1/2 binary64) y) z)
(+ z (+ (* 1/2 x) (* x y)))
(fma.f64 x (+.f64 #s(literal 1/2 binary64) y) z)
(* x y)
(*.f64 x y)
(* y (+ x (+ (* 1/2 (/ x y)) (/ z y))))
(fma.f64 x (+.f64 #s(literal 1/2 binary64) y) z)
(* y (+ x (+ (* 1/2 (/ x y)) (/ z y))))
(fma.f64 x (+.f64 #s(literal 1/2 binary64) y) z)
(* y (+ x (+ (* 1/2 (/ x y)) (/ z y))))
(fma.f64 x (+.f64 #s(literal 1/2 binary64) y) z)
(* x y)
(*.f64 x y)
(* -1 (* y (+ (* -1 x) (* -1 (/ (+ z (* 1/2 x)) y)))))
(fma.f64 x (+.f64 #s(literal 1/2 binary64) y) z)
(* -1 (* y (+ (* -1 x) (* -1 (/ (+ z (* 1/2 x)) y)))))
(fma.f64 x (+.f64 #s(literal 1/2 binary64) y) z)
(* -1 (* y (+ (* -1 x) (* -1 (/ (+ z (* 1/2 x)) y)))))
(fma.f64 x (+.f64 #s(literal 1/2 binary64) y) z)
z
(+ z (* x (+ 1/2 y)))
(fma.f64 x (+.f64 #s(literal 1/2 binary64) y) z)
(+ z (* x (+ 1/2 y)))
(fma.f64 x (+.f64 #s(literal 1/2 binary64) y) z)
(+ z (* x (+ 1/2 y)))
(fma.f64 x (+.f64 #s(literal 1/2 binary64) y) z)
(* x (+ 1/2 y))
(*.f64 x (+.f64 #s(literal 1/2 binary64) y))
(* x (+ 1/2 (+ y (/ z x))))
(fma.f64 x (+.f64 #s(literal 1/2 binary64) y) z)
(* x (+ 1/2 (+ y (/ z x))))
(fma.f64 x (+.f64 #s(literal 1/2 binary64) y) z)
(* x (+ 1/2 (+ y (/ z x))))
(fma.f64 x (+.f64 #s(literal 1/2 binary64) y) z)
(* x (+ 1/2 y))
(*.f64 x (+.f64 #s(literal 1/2 binary64) y))
(* -1 (* x (+ (* -1 (+ 1/2 y)) (* -1 (/ z x)))))
(fma.f64 x (+.f64 #s(literal 1/2 binary64) y) z)
(* -1 (* x (+ (* -1 (+ 1/2 y)) (* -1 (/ z x)))))
(fma.f64 x (+.f64 #s(literal 1/2 binary64) y) z)
(* -1 (* x (+ (* -1 (+ 1/2 y)) (* -1 (/ z x)))))
(fma.f64 x (+.f64 #s(literal 1/2 binary64) y) z)
(* x (+ 1/2 y))
(*.f64 x (+.f64 #s(literal 1/2 binary64) y))
(+ z (* x (+ 1/2 y)))
(fma.f64 x (+.f64 #s(literal 1/2 binary64) y) z)
(+ z (* x (+ 1/2 y)))
(fma.f64 x (+.f64 #s(literal 1/2 binary64) y) z)
(+ z (* x (+ 1/2 y)))
(fma.f64 x (+.f64 #s(literal 1/2 binary64) y) z)
z
(* z (+ 1 (/ (* x (+ 1/2 y)) z)))
(fma.f64 x (+.f64 #s(literal 1/2 binary64) y) z)
(* z (+ 1 (/ (* x (+ 1/2 y)) z)))
(fma.f64 x (+.f64 #s(literal 1/2 binary64) y) z)
(* z (+ 1 (/ (* x (+ 1/2 y)) z)))
(fma.f64 x (+.f64 #s(literal 1/2 binary64) y) z)
z
(* -1 (* z (- (* -1 (/ (* x (+ 1/2 y)) z)) 1)))
(fma.f64 x (+.f64 #s(literal 1/2 binary64) y) z)
(* -1 (* z (- (* -1 (/ (* x (+ 1/2 y)) z)) 1)))
(fma.f64 x (+.f64 #s(literal 1/2 binary64) y) z)
(* -1 (* z (- (* -1 (/ (* x (+ 1/2 y)) z)) 1)))
(fma.f64 x (+.f64 #s(literal 1/2 binary64) y) z)
1/2
#s(literal 1/2 binary64)
(+ 1/2 y)
(+.f64 #s(literal 1/2 binary64) y)
(+ 1/2 y)
(+.f64 #s(literal 1/2 binary64) y)
(+ 1/2 y)
(+.f64 #s(literal 1/2 binary64) y)
y
(* y (+ 1 (* 1/2 (/ 1 y))))
(+.f64 #s(literal 1/2 binary64) y)
(* y (+ 1 (* 1/2 (/ 1 y))))
(+.f64 #s(literal 1/2 binary64) y)
(* y (+ 1 (* 1/2 (/ 1 y))))
(+.f64 #s(literal 1/2 binary64) y)
y
(* y (+ 1 (* 1/2 (/ 1 y))))
(+.f64 #s(literal 1/2 binary64) y)
(* y (+ 1 (* 1/2 (/ 1 y))))
(+.f64 #s(literal 1/2 binary64) y)
(* y (+ 1 (* 1/2 (/ 1 y))))
(+.f64 #s(literal 1/2 binary64) y)
(* x y)
(*.f64 x y)
(* x y)
(*.f64 x y)
(* x y)
(*.f64 x y)
(* x y)
(*.f64 x y)
(* x y)
(*.f64 x y)
(* x y)
(*.f64 x y)
(* x y)
(*.f64 x y)
(* x y)
(*.f64 x y)
(* x y)
(*.f64 x y)
(* x y)
(*.f64 x y)
(* x y)
(*.f64 x y)
(* x y)
(*.f64 x y)
(* x y)
(*.f64 x y)
(* x y)
(*.f64 x y)
(* x y)
(*.f64 x y)
(* x y)
(*.f64 x y)
(* x y)
(*.f64 x y)
(* x y)
(*.f64 x y)
(* x y)
(*.f64 x y)
(* x y)
(*.f64 x y)
(* x y)
(*.f64 x y)
(* x y)
(*.f64 x y)
(* x y)
(*.f64 x y)
(* x y)
(*.f64 x y)
z
(+ z (* 1/2 x))
(fma.f64 #s(literal 1/2 binary64) x z)
(+ z (* 1/2 x))
(fma.f64 #s(literal 1/2 binary64) x z)
(+ z (* 1/2 x))
(fma.f64 #s(literal 1/2 binary64) x z)
(* 1/2 x)
(*.f64 #s(literal 1/2 binary64) x)
(* x (+ 1/2 (/ z x)))
(fma.f64 #s(literal 1/2 binary64) x z)
(* x (+ 1/2 (/ z x)))
(fma.f64 #s(literal 1/2 binary64) x z)
(* x (+ 1/2 (/ z x)))
(fma.f64 #s(literal 1/2 binary64) x z)
(* 1/2 x)
(*.f64 #s(literal 1/2 binary64) x)
(* -1 (* x (- (* -1 (/ z x)) 1/2)))
(fma.f64 #s(literal 1/2 binary64) x z)
(* -1 (* x (- (* -1 (/ z x)) 1/2)))
(fma.f64 #s(literal 1/2 binary64) x z)
(* -1 (* x (- (* -1 (/ z x)) 1/2)))
(fma.f64 #s(literal 1/2 binary64) x z)
(* 1/2 x)
(*.f64 #s(literal 1/2 binary64) x)
(+ z (* 1/2 x))
(fma.f64 #s(literal 1/2 binary64) x z)
(+ z (* 1/2 x))
(fma.f64 #s(literal 1/2 binary64) x z)
(+ z (* 1/2 x))
(fma.f64 #s(literal 1/2 binary64) x z)
z
(* z (+ 1 (* 1/2 (/ x z))))
(fma.f64 #s(literal 1/2 binary64) x z)
(* z (+ 1 (* 1/2 (/ x z))))
(fma.f64 #s(literal 1/2 binary64) x z)
(* z (+ 1 (* 1/2 (/ x z))))
(fma.f64 #s(literal 1/2 binary64) x z)
z
(* -1 (* z (- (* -1/2 (/ x z)) 1)))
(fma.f64 #s(literal 1/2 binary64) x z)
(* -1 (* z (- (* -1/2 (/ x z)) 1)))
(fma.f64 #s(literal 1/2 binary64) x z)
(* -1 (* z (- (* -1/2 (/ x z)) 1)))
(fma.f64 #s(literal 1/2 binary64) x z)
(* x (+ 1/2 y))
(*.f64 x (+.f64 #s(literal 1/2 binary64) y))
(* x (+ 1/2 y))
(*.f64 x (+.f64 #s(literal 1/2 binary64) y))
(* x (+ 1/2 y))
(*.f64 x (+.f64 #s(literal 1/2 binary64) y))
(* x (+ 1/2 y))
(*.f64 x (+.f64 #s(literal 1/2 binary64) y))
(* x (+ 1/2 y))
(*.f64 x (+.f64 #s(literal 1/2 binary64) y))
(* x (+ 1/2 y))
(*.f64 x (+.f64 #s(literal 1/2 binary64) y))
(* x (+ 1/2 y))
(*.f64 x (+.f64 #s(literal 1/2 binary64) y))
(* x (+ 1/2 y))
(*.f64 x (+.f64 #s(literal 1/2 binary64) y))
(* x (+ 1/2 y))
(*.f64 x (+.f64 #s(literal 1/2 binary64) y))
(* x (+ 1/2 y))
(*.f64 x (+.f64 #s(literal 1/2 binary64) y))
(* x (+ 1/2 y))
(*.f64 x (+.f64 #s(literal 1/2 binary64) y))
(* x (+ 1/2 y))
(*.f64 x (+.f64 #s(literal 1/2 binary64) y))
(* 1/2 x)
(*.f64 #s(literal 1/2 binary64) x)
(+ (* 1/2 x) (* x y))
(*.f64 x (+.f64 #s(literal 1/2 binary64) y))
(+ (* 1/2 x) (* x y))
(*.f64 x (+.f64 #s(literal 1/2 binary64) y))
(+ (* 1/2 x) (* x y))
(*.f64 x (+.f64 #s(literal 1/2 binary64) y))
(* x y)
(*.f64 x y)
(* y (+ x (* 1/2 (/ x y))))
(*.f64 x (+.f64 #s(literal 1/2 binary64) y))
(* y (+ x (* 1/2 (/ x y))))
(*.f64 x (+.f64 #s(literal 1/2 binary64) y))
(* y (+ x (* 1/2 (/ x y))))
(*.f64 x (+.f64 #s(literal 1/2 binary64) y))
(* x y)
(*.f64 x y)
(* -1 (* y (+ (* -1 x) (* -1/2 (/ x y)))))
(*.f64 x (+.f64 #s(literal 1/2 binary64) y))
(* -1 (* y (+ (* -1 x) (* -1/2 (/ x y)))))
(*.f64 x (+.f64 #s(literal 1/2 binary64) y))
(* -1 (* y (+ (* -1 x) (* -1/2 (/ x y)))))
(*.f64 x (+.f64 #s(literal 1/2 binary64) y))
1/2
#s(literal 1/2 binary64)
(+ 1/2 y)
(+.f64 #s(literal 1/2 binary64) y)
(+ 1/2 y)
(+.f64 #s(literal 1/2 binary64) y)
(+ 1/2 y)
(+.f64 #s(literal 1/2 binary64) y)
y
(* y (+ 1 (* 1/2 (/ 1 y))))
(+.f64 #s(literal 1/2 binary64) y)
(* y (+ 1 (* 1/2 (/ 1 y))))
(+.f64 #s(literal 1/2 binary64) y)
(* y (+ 1 (* 1/2 (/ 1 y))))
(+.f64 #s(literal 1/2 binary64) y)
y
(* y (+ 1 (* 1/2 (/ 1 y))))
(+.f64 #s(literal 1/2 binary64) y)
(* y (+ 1 (* 1/2 (/ 1 y))))
(+.f64 #s(literal 1/2 binary64) y)
(* y (+ 1 (* 1/2 (/ 1 y))))
(+.f64 #s(literal 1/2 binary64) y)
z
(+ z (* x y))
(fma.f64 x y z)
(+ z (* x y))
(fma.f64 x y z)
(+ z (* x y))
(fma.f64 x y z)
(* x y)
(*.f64 x y)
(* x (+ y (/ z x)))
(fma.f64 x y z)
(* x (+ y (/ z x)))
(fma.f64 x y z)
(* x (+ y (/ z x)))
(fma.f64 x y z)
(* x y)
(*.f64 x y)
(* -1 (* x (+ (* -1 y) (* -1 (/ z x)))))
(fma.f64 x y z)
(* -1 (* x (+ (* -1 y) (* -1 (/ z x)))))
(fma.f64 x y z)
(* -1 (* x (+ (* -1 y) (* -1 (/ z x)))))
(fma.f64 x y z)
z
(+ z (* x y))
(fma.f64 x y z)
(+ z (* x y))
(fma.f64 x y z)
(+ z (* x y))
(fma.f64 x y z)
(* x y)
(*.f64 x y)
(* y (+ x (/ z y)))
(fma.f64 x y z)
(* y (+ x (/ z y)))
(fma.f64 x y z)
(* y (+ x (/ z y)))
(fma.f64 x y z)
(* x y)
(*.f64 x y)
(* -1 (* y (+ (* -1 x) (* -1 (/ z y)))))
(fma.f64 x y z)
(* -1 (* y (+ (* -1 x) (* -1 (/ z y)))))
(fma.f64 x y z)
(* -1 (* y (+ (* -1 x) (* -1 (/ z y)))))
(fma.f64 x y z)
(* x y)
(*.f64 x y)
(+ z (* x y))
(fma.f64 x y z)
(+ z (* x y))
(fma.f64 x y z)
(+ z (* x y))
(fma.f64 x y z)
z
(* z (+ 1 (/ (* x y) z)))
(fma.f64 x y z)
(* z (+ 1 (/ (* x y) z)))
(fma.f64 x y z)
(* z (+ 1 (/ (* x y) z)))
(fma.f64 x y z)
z
(* -1 (* z (- (* -1 (/ (* x y) z)) 1)))
(fma.f64 x y z)
(* -1 (* z (- (* -1 (/ (* x y) z)) 1)))
(fma.f64 x y z)
(* -1 (* z (- (* -1 (/ (* x y) z)) 1)))
(fma.f64 x y z)

eval157.0ms (2.6%)

Memory: -14.0MiB live, 105.3MiB allocated
Compiler: Compiled 14 466 to 1 125 computations (92.2% saved)

prune209.0ms (3.5%)

Memory

-13.6MiB live, 108.4MiB allocated

Pruning

6 alts after pruning (2 fresh and 4 done)

	Pruned	Kept	Total
New	656	2	658
Fresh	0	0	0
Picked	1	4	5
Done	0	0	0
Total	657	6	663

Accuracy

100.0%

Counts

663 → 6

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	100.0%	(fma.f64 (+.f64 y #s(literal 1/2 binary64)) x z)
▶	78.0%	(fma.f64 y x z)
✓	61.3%	(fma.f64 x #s(literal 1/2 binary64) z)
✓	61.4%	(*.f64 x (+.f64 #s(literal 1/2 binary64) y))
✓	39.8%	(*.f64 x y)
▶	23.1%	(*.f64 x #s(literal 1/2 binary64))

Compiler

Compiled 43 to 30 computations (30.2% saved)

simplify5.0ms (0.1%)

Memory

4.7MiB live, 4.7MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 2 expressions of interest:

New	Metric	Score	Program
✓	cost-diff	0	(fma.f64 y x z)
✓	cost-diff	0	(*.f64 x #s(literal 1/2 binary64))

Rules

8×	`lower-*.f32`
6×	`lower-*.f64`
4×	`*-commutative`
4×	`lower-+.f64`
4×	`lower-fma.f32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	6	12
0	9	12
1	12	12
0	12	12

Stop Event

1×	iter limit
1×	saturated
1×	iter limit

Calls

Call 1

Inputs
(*.f64 x #s(literal 1/2 binary64))
x
#s(literal 1/2 binary64)
(fma.f64 y x z)
y
x
z

Outputs
(*.f64 x #s(literal 1/2 binary64))
x
#s(literal 1/2 binary64)
(fma.f64 y x z)
(fma.f64 x y z)
y
x
z

localize18.0ms (0.3%)

Memory

22.8MiB live, 22.8MiB allocated

Localize:

Found 2 expressions of interest:

New	Metric	Score	Program
✓	accuracy	100.0%	(fma.f64 y x z)
✓	accuracy	100.0%	(*.f64 x #s(literal 1/2 binary64))

Samples

12.0ms

256×

valid

Compiler

Compiled 15 to 9 computations (40% saved)

Precisions

Click to see histograms. Total time spent on operations: 5.0ms

ival-mult: 3.0ms (63.1% of total)

ival-add: 1.0ms (21% of total)

ival-true: 0.0ms (0% of total)

exact: 0.0ms (0% of total)

ival-assert: 0.0ms (0% of total)

series1.0ms (0%)

Memory

1.0MiB live, 1.0MiB allocated

Counts

2 → 48

Calls

Call 1

Inputs
#<alt (*.f64 x #s(literal 1/2 binary64))>
#<alt (fma.f64 y x z)>

Outputs
#<alt (* 1/2 x)>
#<alt (* 1/2 x)>
#<alt (* 1/2 x)>
#<alt (* 1/2 x)>
#<alt (* 1/2 x)>
#<alt (* 1/2 x)>
#<alt (* 1/2 x)>
#<alt (* 1/2 x)>
#<alt (* 1/2 x)>
#<alt (* 1/2 x)>
#<alt (* 1/2 x)>
#<alt (* 1/2 x)>
#<alt z>
#<alt (+ z (* x y))>
#<alt (+ z (* x y))>
#<alt (+ z (* x y))>
#<alt (* x y)>
#<alt (* y (+ x (/ z y)))>
#<alt (* y (+ x (/ z y)))>
#<alt (* y (+ x (/ z y)))>
#<alt (* x y)>
#<alt (* -1 (* y (+ (* -1 x) (* -1 (/ z y)))))>
#<alt (* -1 (* y (+ (* -1 x) (* -1 (/ z y)))))>
#<alt (* -1 (* y (+ (* -1 x) (* -1 (/ z y)))))>
#<alt z>
#<alt (+ z (* x y))>
#<alt (+ z (* x y))>
#<alt (+ z (* x y))>
#<alt (* x y)>
#<alt (* x (+ y (/ z x)))>
#<alt (* x (+ y (/ z x)))>
#<alt (* x (+ y (/ z x)))>
#<alt (* x y)>
#<alt (* -1 (* x (+ (* -1 y) (* -1 (/ z x)))))>
#<alt (* -1 (* x (+ (* -1 y) (* -1 (/ z x)))))>
#<alt (* -1 (* x (+ (* -1 y) (* -1 (/ z x)))))>
#<alt (* x y)>
#<alt (+ z (* x y))>
#<alt (+ z (* x y))>
#<alt (+ z (* x y))>
#<alt z>
#<alt (* z (+ 1 (/ (* x y) z)))>
#<alt (* z (+ 1 (/ (* x y) z)))>
#<alt (* z (+ 1 (/ (* x y) z)))>
#<alt z>
#<alt (* -1 (* z (- (* -1 (/ (* x y) z)) 1)))>
#<alt (* -1 (* z (- (* -1 (/ (* x y) z)) 1)))>
#<alt (* -1 (* z (- (* -1 (/ (* x y) z)) 1)))>

Calls

12 calls:

Time	Variable		Point	Expression
0.0ms	x	@	0	(* x 1/2)
0.0ms	y	@	-inf	(+ (* y x) z)
0.0ms	x	@	-inf	(+ (* y x) z)
0.0ms	z	@	inf	(+ (* y x) z)
0.0ms	y	@	0	(+ (* y x) z)

rewrite634.0ms (10.5%)

Memory

0.0MiB live, 762.1MiB allocated

Algorithm

1×	batch-egg-rewrite

Rules

18 338×	`lower-fma.f32`
18 336×	`lower-fma.f64`
4 376×	`lower-*.f32`
4 374×	`lower-*.f64`
3 924×	`lower-/.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	6	7
0	9	7
1	25	7
2	155	7
3	1493	7
0	8263	7

Stop Event

1×	iter limit
1×	node limit
1×	iter limit

Counts

2 → 213

Calls

Call 1

Inputs
(*.f64 x #s(literal 1/2 binary64))
(fma.f64 y x z)

Outputs
(*.f64 x #s(literal 1/2 binary64))
(*.f64 #s(literal 1/2 binary64) x)
(+.f64 z (*.f64 x y))
(+.f64 (*.f64 x y) z)
(+.f64 (.f64 x y) (.f64 #s(literal 1 binary64) z))
(+.f64 (/.f64 (.f64 x (.f64 x (.f64 y y))) (-.f64 (.f64 x y) z)) (neg.f64 (/.f64 (.f64 z z) (-.f64 (.f64 x y) z))))
(+.f64 (/.f64 (.f64 x (.f64 x (.f64 y y))) (-.f64 (.f64 x y) z)) (.f64 (neg.f64 z) (/.f64 z (-.f64 (.f64 x y) z))))
(+.f64 (/.f64 (.f64 x (.f64 x (.f64 y y))) (-.f64 (.f64 x y) z)) (.f64 (neg.f64 (.f64 z z)) (/.f64 #s(literal 1 binary64) (-.f64 (*.f64 x y) z))))
(+.f64 (/.f64 (.f64 x (.f64 x (.f64 y y))) (-.f64 (.f64 x y) z)) (.f64 (neg.f64 (/.f64 (.f64 z z) (.f64 (fma.f64 x y z) (-.f64 (.f64 x y) z)))) (fma.f64 x y z)))
(+.f64 (/.f64 (.f64 x (.f64 x (.f64 y y))) (-.f64 (.f64 x y) z)) (.f64 (neg.f64 (/.f64 (.f64 z z) (-.f64 (.f64 (.f64 x y) (.f64 x (.f64 x (.f64 y y)))) (.f64 z (.f64 z z))))) (fma.f64 x (.f64 x (.f64 y y)) (.f64 z (fma.f64 x y z)))))
(+.f64 (/.f64 (.f64 z z) (-.f64 z (.f64 x y))) (neg.f64 (/.f64 (.f64 x (.f64 x (.f64 y y))) (-.f64 z (.f64 x y)))))
(exp.f64 (*.f64 (log.f64 (/.f64 #s(literal 1 binary64) (fma.f64 x y z))) #s(literal -1 binary64)))
(-.f64 (*.f64 x y) (neg.f64 z))
(-.f64 (/.f64 (.f64 x (.f64 x (.f64 y y))) (-.f64 (.f64 x y) z)) (/.f64 (.f64 z z) (-.f64 (.f64 x y) z)))
(-.f64 #s(literal 0 binary64) (neg.f64 (fma.f64 x y z)))
(-.f64 (/.f64 (.f64 z z) (-.f64 z (.f64 x y))) (/.f64 (.f64 x (.f64 x (.f64 y y))) (-.f64 z (.f64 x y))))
(-.f64 (/.f64 #s(literal 0 binary64) (fma.f64 x (neg.f64 y) z)) (neg.f64 (fma.f64 x y z)))
(-.f64 (/.f64 (/.f64 (.f64 (.f64 (.f64 x y) (.f64 x (.f64 x (.f64 y y)))) (.f64 (.f64 x y) (.f64 x (.f64 x (.f64 y y))))) (-.f64 (.f64 (.f64 x y) (.f64 x (.f64 x (.f64 y y)))) (.f64 z (.f64 z z)))) (fma.f64 (.f64 x y) (-.f64 (.f64 x y) z) (.f64 z z))) (/.f64 (/.f64 (.f64 (.f64 z (.f64 z z)) (.f64 z (.f64 z z))) (-.f64 (.f64 (.f64 x y) (.f64 x (.f64 x (.f64 y y)))) (.f64 z (.f64 z z)))) (fma.f64 (.f64 x y) (-.f64 (.f64 x y) z) (.f64 z z))))
(-.f64 (/.f64 (/.f64 (.f64 (.f64 (.f64 x y) (.f64 x (.f64 x (.f64 y y)))) (.f64 (.f64 x y) (.f64 x (.f64 x (.f64 y y))))) (fma.f64 x (.f64 (.f64 x (.f64 y y)) (.f64 x (.f64 x (.f64 y y)))) (.f64 (.f64 z z) (fma.f64 y (.f64 x (.f64 x y)) (.f64 z z))))) (-.f64 (.f64 x y) z)) (/.f64 (/.f64 (.f64 (.f64 z (.f64 z z)) (.f64 z (.f64 z z))) (fma.f64 x (.f64 (.f64 x (.f64 y y)) (.f64 x (.f64 x (.f64 y y)))) (.f64 (.f64 z z) (fma.f64 y (.f64 x (.f64 x y)) (.f64 z z))))) (-.f64 (.f64 x y) z)))
(-.f64 (/.f64 (/.f64 (.f64 x (.f64 (.f64 x (.f64 y y)) (.f64 x (.f64 x (.f64 y y))))) (fma.f64 y (.f64 x (.f64 x y)) (.f64 z z))) (-.f64 (.f64 x y) z)) (/.f64 (/.f64 (.f64 z (.f64 z (.f64 z z))) (fma.f64 y (.f64 x (.f64 x y)) (.f64 z z))) (-.f64 (.f64 x y) z)))
(-.f64 (/.f64 #s(literal 0 binary64) (neg.f64 (fma.f64 (.f64 x y) (-.f64 (.f64 x y) z) (*.f64 z z)))) (neg.f64 (fma.f64 x y z)))
(-.f64 (/.f64 (.f64 (.f64 (.f64 x y) (.f64 x (.f64 x (.f64 y y)))) (.f64 (.f64 x y) (.f64 x (.f64 x (.f64 y y))))) (.f64 (fma.f64 (.f64 x y) (-.f64 (.f64 x y) z) (.f64 z z)) (-.f64 (.f64 (.f64 x y) (.f64 x (.f64 x (.f64 y y)))) (.f64 z (.f64 z z))))) (/.f64 (.f64 (.f64 z (.f64 z z)) (.f64 z (.f64 z z))) (.f64 (fma.f64 (.f64 x y) (-.f64 (.f64 x y) z) (.f64 z z)) (-.f64 (.f64 (.f64 x y) (.f64 x (.f64 x (.f64 y y)))) (.f64 z (.f64 z z))))))
(-.f64 (/.f64 (.f64 (.f64 (.f64 x y) (.f64 x (.f64 x (.f64 y y)))) (.f64 (.f64 x y) (.f64 x (.f64 x (.f64 y y))))) (.f64 (-.f64 (.f64 x y) z) (fma.f64 x (.f64 (.f64 x (.f64 y y)) (.f64 x (.f64 x (.f64 y y)))) (.f64 (.f64 z z) (fma.f64 y (.f64 x (.f64 x y)) (.f64 z z)))))) (/.f64 (.f64 (.f64 z (.f64 z z)) (.f64 z (.f64 z z))) (.f64 (-.f64 (.f64 x y) z) (fma.f64 x (.f64 (.f64 x (.f64 y y)) (.f64 x (.f64 x (.f64 y y)))) (.f64 (.f64 z z) (fma.f64 y (.f64 x (.f64 x y)) (.f64 z z)))))))
(-.f64 (/.f64 (.f64 x (.f64 (.f64 x (.f64 y y)) (.f64 x (.f64 x (.f64 y y))))) (.f64 (-.f64 (.f64 x y) z) (fma.f64 y (.f64 x (.f64 x y)) (.f64 z z)))) (/.f64 (.f64 z (.f64 z (.f64 z z))) (.f64 (-.f64 (.f64 x y) z) (fma.f64 y (.f64 x (.f64 x y)) (.f64 z z)))))
(-.f64 (/.f64 (.f64 (.f64 x (.f64 x (.f64 y y))) (-.f64 (.f64 x y) z)) (.f64 (-.f64 (.f64 x y) z) (-.f64 (.f64 x y) z))) (/.f64 (.f64 (-.f64 (.f64 x y) z) (.f64 z z)) (.f64 (-.f64 (.f64 x y) z) (-.f64 (.f64 x y) z))))
(-.f64 (/.f64 (.f64 (/.f64 (.f64 x (.f64 x (.f64 y y))) (-.f64 (.f64 x y) z)) (.f64 (/.f64 (.f64 x (.f64 x (.f64 y y))) (-.f64 (.f64 x y) z)) (/.f64 (.f64 x (.f64 x (.f64 y y))) (-.f64 (.f64 x y) z)))) (fma.f64 (.f64 x (.f64 x (.f64 y y))) (.f64 (/.f64 (.f64 x y) (-.f64 (.f64 x y) z)) (/.f64 (.f64 x y) (-.f64 (.f64 x y) z))) (fma.f64 (.f64 z z) (.f64 (/.f64 z (-.f64 (.f64 x y) z)) (/.f64 z (-.f64 (.f64 x y) z))) (.f64 (/.f64 (.f64 x (.f64 x (.f64 y y))) (-.f64 (.f64 x y) z)) (/.f64 (.f64 z z) (-.f64 (.f64 x y) z)))))) (/.f64 (.f64 (/.f64 (.f64 z z) (-.f64 (.f64 x y) z)) (.f64 (.f64 z z) (.f64 (/.f64 z (-.f64 (.f64 x y) z)) (/.f64 z (-.f64 (.f64 x y) z))))) (fma.f64 (.f64 x (.f64 x (.f64 y y))) (.f64 (/.f64 (.f64 x y) (-.f64 (.f64 x y) z)) (/.f64 (.f64 x y) (-.f64 (.f64 x y) z))) (fma.f64 (.f64 z z) (.f64 (/.f64 z (-.f64 (.f64 x y) z)) (/.f64 z (-.f64 (.f64 x y) z))) (.f64 (/.f64 (.f64 x (.f64 x (.f64 y y))) (-.f64 (.f64 x y) z)) (/.f64 (.f64 z z) (-.f64 (.f64 x y) z)))))))
(-.f64 (/.f64 (.f64 (/.f64 (.f64 x (.f64 x (.f64 y y))) (-.f64 (.f64 x y) z)) (/.f64 (.f64 x (.f64 x (.f64 y y))) (-.f64 (.f64 x y) z))) (fma.f64 x (/.f64 (.f64 x (.f64 y y)) (-.f64 (.f64 x y) z)) (/.f64 (.f64 z z) (-.f64 (.f64 x y) z)))) (/.f64 (.f64 (.f64 z z) (.f64 (/.f64 z (-.f64 (.f64 x y) z)) (/.f64 z (-.f64 (.f64 x y) z)))) (fma.f64 x (/.f64 (.f64 x (.f64 y y)) (-.f64 (.f64 x y) z)) (/.f64 (.f64 z z) (-.f64 (.f64 x y) z)))))
(fma.f64 x y z)
(fma.f64 x y (*.f64 #s(literal 1 binary64) z))
(fma.f64 x (/.f64 (.f64 x (.f64 y y)) (-.f64 (.f64 x y) z)) (neg.f64 (/.f64 (.f64 z z) (-.f64 (*.f64 x y) z))))
(fma.f64 x (/.f64 (.f64 x (.f64 y y)) (-.f64 (.f64 x y) z)) (.f64 (neg.f64 z) (/.f64 z (-.f64 (*.f64 x y) z))))
(fma.f64 x (/.f64 (.f64 x (.f64 y y)) (-.f64 (.f64 x y) z)) (.f64 (neg.f64 (.f64 z z)) (/.f64 #s(literal 1 binary64) (-.f64 (.f64 x y) z))))
(fma.f64 x (/.f64 (.f64 x (.f64 y y)) (-.f64 (.f64 x y) z)) (.f64 (neg.f64 (/.f64 (.f64 z z) (.f64 (fma.f64 x y z) (-.f64 (*.f64 x y) z)))) (fma.f64 x y z)))
(fma.f64 x (/.f64 (.f64 x (.f64 y y)) (-.f64 (.f64 x y) z)) (.f64 (neg.f64 (/.f64 (.f64 z z) (-.f64 (.f64 (.f64 x y) (.f64 x (.f64 x (.f64 y y)))) (.f64 z (.f64 z z))))) (fma.f64 x (.f64 x (.f64 y y)) (*.f64 z (fma.f64 x y z)))))
(fma.f64 y x z)
(fma.f64 y x (*.f64 #s(literal 1 binary64) z))
(fma.f64 y (/.f64 (.f64 x (.f64 x y)) (-.f64 (.f64 x y) z)) (neg.f64 (/.f64 (.f64 z z) (-.f64 (*.f64 x y) z))))
(fma.f64 y (/.f64 (.f64 x (.f64 x y)) (-.f64 (.f64 x y) z)) (.f64 (neg.f64 z) (/.f64 z (-.f64 (*.f64 x y) z))))
(fma.f64 y (/.f64 (.f64 x (.f64 x y)) (-.f64 (.f64 x y) z)) (.f64 (neg.f64 (.f64 z z)) (/.f64 #s(literal 1 binary64) (-.f64 (.f64 x y) z))))
(fma.f64 y (/.f64 (.f64 x (.f64 x y)) (-.f64 (.f64 x y) z)) (.f64 (neg.f64 (/.f64 (.f64 z z) (.f64 (fma.f64 x y z) (-.f64 (*.f64 x y) z)))) (fma.f64 x y z)))
(fma.f64 y (/.f64 (.f64 x (.f64 x y)) (-.f64 (.f64 x y) z)) (.f64 (neg.f64 (/.f64 (.f64 z z) (-.f64 (.f64 (.f64 x y) (.f64 x (.f64 x (.f64 y y)))) (.f64 z (.f64 z z))))) (fma.f64 x (.f64 x (.f64 y y)) (*.f64 z (fma.f64 x y z)))))
(fma.f64 (.f64 x y) (/.f64 (.f64 x y) (-.f64 (.f64 x y) z)) (neg.f64 (/.f64 (.f64 z z) (-.f64 (*.f64 x y) z))))
(fma.f64 (.f64 x y) (/.f64 (.f64 x y) (-.f64 (.f64 x y) z)) (.f64 (neg.f64 z) (/.f64 z (-.f64 (*.f64 x y) z))))
(fma.f64 (.f64 x y) (/.f64 (.f64 x y) (-.f64 (.f64 x y) z)) (.f64 (neg.f64 (.f64 z z)) (/.f64 #s(literal 1 binary64) (-.f64 (.f64 x y) z))))
(fma.f64 (.f64 x y) (/.f64 (.f64 x y) (-.f64 (.f64 x y) z)) (.f64 (neg.f64 (/.f64 (.f64 z z) (.f64 (fma.f64 x y z) (-.f64 (*.f64 x y) z)))) (fma.f64 x y z)))
(fma.f64 (.f64 x y) (/.f64 (.f64 x y) (-.f64 (.f64 x y) z)) (.f64 (neg.f64 (/.f64 (.f64 z z) (-.f64 (.f64 (.f64 x y) (.f64 x (.f64 x (.f64 y y)))) (.f64 z (.f64 z z))))) (fma.f64 x (.f64 x (.f64 y y)) (*.f64 z (fma.f64 x y z)))))
(fma.f64 (.f64 x (.f64 x (.f64 y y))) (/.f64 #s(literal 1 binary64) (-.f64 (.f64 x y) z)) (neg.f64 (/.f64 (.f64 z z) (-.f64 (.f64 x y) z))))
(fma.f64 (.f64 x (.f64 x (.f64 y y))) (/.f64 #s(literal 1 binary64) (-.f64 (.f64 x y) z)) (.f64 (neg.f64 z) (/.f64 z (-.f64 (.f64 x y) z))))
(fma.f64 (.f64 x (.f64 x (.f64 y y))) (/.f64 #s(literal 1 binary64) (-.f64 (.f64 x y) z)) (.f64 (neg.f64 (.f64 z z)) (/.f64 #s(literal 1 binary64) (-.f64 (*.f64 x y) z))))
(fma.f64 (.f64 x (.f64 x (.f64 y y))) (/.f64 #s(literal 1 binary64) (-.f64 (.f64 x y) z)) (.f64 (neg.f64 (/.f64 (.f64 z z) (.f64 (fma.f64 x y z) (-.f64 (.f64 x y) z)))) (fma.f64 x y z)))
(fma.f64 (.f64 x (.f64 x (.f64 y y))) (/.f64 #s(literal 1 binary64) (-.f64 (.f64 x y) z)) (.f64 (neg.f64 (/.f64 (.f64 z z) (-.f64 (.f64 (.f64 x y) (.f64 x (.f64 x (.f64 y y)))) (.f64 z (.f64 z z))))) (fma.f64 x (.f64 x (.f64 y y)) (.f64 z (fma.f64 x y z)))))
(fma.f64 (.f64 z z) (/.f64 #s(literal 1 binary64) (-.f64 z (.f64 x y))) (neg.f64 (/.f64 (.f64 x (.f64 x (.f64 y y))) (-.f64 z (.f64 x y)))))
(fma.f64 #s(literal 1 binary64) (/.f64 (.f64 x (.f64 x (.f64 y y))) (-.f64 (.f64 x y) z)) (neg.f64 (/.f64 (.f64 z z) (-.f64 (.f64 x y) z))))
(fma.f64 #s(literal 1 binary64) (/.f64 (.f64 x (.f64 x (.f64 y y))) (-.f64 (.f64 x y) z)) (.f64 (neg.f64 z) (/.f64 z (-.f64 (.f64 x y) z))))
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(.f64 (fma.f64 (.f64 (.f64 x y) (.f64 x (.f64 x (.f64 y y)))) (.f64 (.f64 (.f64 x y) (.f64 x (.f64 x (.f64 y y)))) (.f64 (.f64 x y) (.f64 x (.f64 x (.f64 y y))))) (.f64 (.f64 z (.f64 z z)) (.f64 (.f64 z (.f64 z z)) (.f64 z (.f64 z z))))) (/.f64 #s(literal 1 binary64) (.f64 (fma.f64 (.f64 (.f64 x y) (.f64 x (.f64 x (.f64 y y)))) (.f64 (.f64 x y) (.f64 x (.f64 x (.f64 y y)))) (.f64 (.f64 z (.f64 z z)) (-.f64 (.f64 z (.f64 z z)) (.f64 (.f64 x y) (.f64 x (.f64 x (.f64 y y))))))) (fma.f64 (.f64 x y) (-.f64 (.f64 x y) z) (*.f64 z z)))))
(*.f64 #s(literal 1 binary64) (fma.f64 x y z))
(.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (.f64 x y) (-.f64 (.f64 x y) z) (.f64 z z))) (.f64 (fma.f64 x y z) (fma.f64 (.f64 x y) (-.f64 (.f64 x y) z) (.f64 z z))))
(.f64 (/.f64 #s(literal 1 binary64) (-.f64 (.f64 x y) z)) (.f64 (fma.f64 x y z) (-.f64 (.f64 x y) z)))
(.f64 (.f64 (.f64 (fma.f64 x y z) (fma.f64 (.f64 x y) (-.f64 (.f64 x y) z) (.f64 z z))) (-.f64 (.f64 (.f64 x y) (.f64 x (.f64 x (.f64 y y)))) (.f64 z (.f64 z z)))) (/.f64 #s(literal 1 binary64) (.f64 (fma.f64 (.f64 x y) (-.f64 (.f64 x y) z) (.f64 z z)) (-.f64 (.f64 (.f64 x y) (.f64 x (.f64 x (.f64 y y)))) (.f64 z (.f64 z z))))))
(.f64 (.f64 (.f64 (fma.f64 x y z) (fma.f64 (.f64 x y) (-.f64 (.f64 x y) z) (.f64 z z))) (-.f64 (.f64 (.f64 x y) (.f64 x (.f64 x (.f64 y y)))) (.f64 z (.f64 z z)))) (/.f64 #s(literal 1 binary64) (.f64 (-.f64 (.f64 x y) z) (fma.f64 x (.f64 (.f64 x (.f64 y y)) (.f64 x (.f64 x (.f64 y y)))) (.f64 (.f64 z z) (fma.f64 y (.f64 x (.f64 x y)) (.f64 z z)))))))
(.f64 (.f64 (.f64 (fma.f64 x y z) (fma.f64 (.f64 x y) (-.f64 (.f64 x y) z) (.f64 z z))) (-.f64 (.f64 (.f64 x y) (.f64 x (.f64 x (.f64 y y)))) (.f64 z (.f64 z z)))) (/.f64 #s(literal 1 binary64) (.f64 (-.f64 (.f64 (.f64 x y) (.f64 x (.f64 x (.f64 y y)))) (.f64 z (.f64 z z))) (fma.f64 (.f64 x y) (-.f64 (.f64 x y) z) (.f64 z z)))))
(.f64 (.f64 (.f64 (fma.f64 x y z) (fma.f64 (.f64 x y) (-.f64 (.f64 x y) z) (.f64 z z))) (-.f64 (.f64 (.f64 x y) (.f64 x (.f64 x (.f64 y y)))) (.f64 z (.f64 z z)))) (/.f64 #s(literal 1 binary64) (.f64 (fma.f64 x (.f64 (.f64 x (.f64 y y)) (.f64 x (.f64 x (.f64 y y)))) (.f64 (.f64 z z) (fma.f64 y (.f64 x (.f64 x y)) (.f64 z z)))) (-.f64 (.f64 x y) z))))
(.f64 (.f64 (fma.f64 x y z) (-.f64 z (.f64 x y))) (/.f64 #s(literal 1 binary64) (-.f64 z (.f64 x y))))
(.f64 (.f64 (.f64 (fma.f64 x y z) (-.f64 (.f64 x y) z)) (fma.f64 y (.f64 x (.f64 x y)) (.f64 z z))) (/.f64 #s(literal 1 binary64) (.f64 (-.f64 (.f64 x y) z) (fma.f64 y (.f64 x (.f64 x y)) (.f64 z z)))))
(.f64 (.f64 (.f64 (fma.f64 x y z) (-.f64 (.f64 x y) z)) (fma.f64 y (.f64 x (.f64 x y)) (.f64 z z))) (/.f64 #s(literal 1 binary64) (.f64 (fma.f64 y (.f64 x (.f64 x y)) (.f64 z z)) (-.f64 (.f64 x y) z))))
(*.f64 #s(literal -1 binary64) (neg.f64 (fma.f64 x y z)))
(*.f64 #s(literal -1 binary64) (/.f64 #s(literal 1 binary64) (neg.f64 (/.f64 #s(literal 1 binary64) (fma.f64 x y z)))))
(.f64 (fma.f64 (.f64 x (.f64 x (.f64 y y))) (-.f64 (.f64 x y) z) (.f64 (fma.f64 x (neg.f64 y) z) (.f64 z z))) (/.f64 #s(literal 1 binary64) (.f64 (-.f64 (.f64 x y) z) (-.f64 (.f64 x y) z))))
(.f64 (neg.f64 (.f64 (fma.f64 x y z) (-.f64 z (.f64 x y)))) (/.f64 #s(literal 1 binary64) (neg.f64 (-.f64 z (.f64 x y)))))
(.f64 (-.f64 (.f64 (/.f64 (.f64 x (.f64 x (.f64 y y))) (-.f64 (.f64 x y) z)) (.f64 (/.f64 (.f64 x (.f64 x (.f64 y y))) (-.f64 (.f64 x y) z)) (/.f64 (.f64 x (.f64 x (.f64 y y))) (-.f64 (.f64 x y) z)))) (.f64 (/.f64 (.f64 z z) (-.f64 (.f64 x y) z)) (.f64 (.f64 z z) (.f64 (/.f64 z (-.f64 (.f64 x y) z)) (/.f64 z (-.f64 (.f64 x y) z)))))) (/.f64 #s(literal 1 binary64) (fma.f64 (.f64 x (.f64 x (.f64 y y))) (.f64 (/.f64 (.f64 x y) (-.f64 (.f64 x y) z)) (/.f64 (.f64 x y) (-.f64 (.f64 x y) z))) (fma.f64 (.f64 z z) (.f64 (/.f64 z (-.f64 (.f64 x y) z)) (/.f64 z (-.f64 (.f64 x y) z))) (.f64 (/.f64 (.f64 x (.f64 x (.f64 y y))) (-.f64 (.f64 x y) z)) (/.f64 (.f64 z z) (-.f64 (.f64 x y) z)))))))
(.f64 (.f64 (fma.f64 x (/.f64 (.f64 x (.f64 y y)) (-.f64 (.f64 x y) z)) (/.f64 (.f64 z z) (-.f64 (.f64 x y) z))) (fma.f64 x y z)) (/.f64 #s(literal 1 binary64) (fma.f64 x (/.f64 (.f64 x (.f64 y y)) (-.f64 (.f64 x y) z)) (/.f64 (.f64 z z) (-.f64 (.f64 x y) z)))))
(.f64 (/.f64 (fma.f64 (.f64 (.f64 x y) (.f64 x (.f64 x (.f64 y y)))) (.f64 (.f64 (.f64 x y) (.f64 x (.f64 x (.f64 y y)))) (.f64 (.f64 x y) (.f64 x (.f64 x (.f64 y y))))) (.f64 (.f64 z (.f64 z z)) (.f64 (.f64 z (.f64 z z)) (.f64 z (.f64 z z))))) (fma.f64 (.f64 x y) (-.f64 (.f64 x y) z) (.f64 z z))) (/.f64 #s(literal 1 binary64) (fma.f64 (.f64 (.f64 x y) (.f64 x (.f64 x (.f64 y y)))) (.f64 (.f64 x y) (.f64 x (.f64 x (.f64 y y)))) (.f64 (.f64 z (.f64 z z)) (-.f64 (.f64 z (.f64 z z)) (.f64 (.f64 x y) (.f64 x (.f64 x (.f64 y y)))))))))
(.f64 (/.f64 (.f64 (.f64 (fma.f64 x y z) (fma.f64 (.f64 x y) (-.f64 (.f64 x y) z) (.f64 z z))) (-.f64 (.f64 (.f64 x y) (.f64 x (.f64 x (.f64 y y)))) (.f64 z (.f64 z z)))) (fma.f64 (.f64 x y) (-.f64 (.f64 x y) z) (.f64 z z))) (/.f64 #s(literal 1 binary64) (-.f64 (.f64 (.f64 x y) (.f64 x (.f64 x (.f64 y y)))) (.f64 z (*.f64 z z)))))
(.f64 (/.f64 (.f64 (.f64 (fma.f64 x y z) (fma.f64 (.f64 x y) (-.f64 (.f64 x y) z) (.f64 z z))) (-.f64 (.f64 (.f64 x y) (.f64 x (.f64 x (.f64 y y)))) (.f64 z (.f64 z z)))) (-.f64 (.f64 x y) z)) (/.f64 #s(literal 1 binary64) (fma.f64 x (.f64 (.f64 x (.f64 y y)) (.f64 x (.f64 x (.f64 y y)))) (.f64 (.f64 z z) (fma.f64 y (.f64 x (.f64 x y)) (*.f64 z z))))))
(.f64 (/.f64 (.f64 (.f64 (fma.f64 x y z) (-.f64 (.f64 x y) z)) (fma.f64 y (.f64 x (.f64 x y)) (.f64 z z))) (-.f64 (.f64 x y) z)) (/.f64 #s(literal 1 binary64) (fma.f64 y (.f64 x (.f64 x y)) (*.f64 z z))))
(.f64 (/.f64 (.f64 (fma.f64 x y z) (fma.f64 (.f64 x y) (-.f64 (.f64 x y) z) (.f64 z z))) (fma.f64 (.f64 (.f64 x y) (.f64 x (.f64 x (.f64 y y)))) (.f64 (.f64 x y) (.f64 x (.f64 x (.f64 y y)))) (.f64 (.f64 z (-.f64 z (.f64 x y))) (.f64 (.f64 z (-.f64 z (.f64 x y))) (.f64 z (-.f64 z (.f64 x y))))))) (fma.f64 x (.f64 (.f64 x (.f64 y y)) (.f64 x (.f64 x (.f64 y y)))) (.f64 (.f64 z (-.f64 z (.f64 x y))) (-.f64 (.f64 z (-.f64 z (.f64 x y))) (.f64 x (.f64 x (*.f64 y y)))))))
(.f64 (/.f64 (.f64 (fma.f64 x y z) (fma.f64 (.f64 x y) (-.f64 (.f64 x y) z) (.f64 z z))) (.f64 (fma.f64 (.f64 x y) (-.f64 (.f64 x y) z) (.f64 z z)) (fma.f64 (fma.f64 x y z) (-.f64 (.f64 x y) z) (.f64 z (.f64 x y))))) (fma.f64 (fma.f64 x y z) (-.f64 (.f64 x y) z) (.f64 z (*.f64 x y))))
(.f64 (/.f64 (.f64 (fma.f64 x y z) (-.f64 (.f64 x y) z)) (-.f64 (.f64 (.f64 x y) (.f64 x (.f64 x (.f64 y y)))) (.f64 z (.f64 z z)))) (fma.f64 x (.f64 x (.f64 y y)) (*.f64 z (fma.f64 x y z))))
(.f64 (pow.f64 (/.f64 (-.f64 (.f64 x y) z) (.f64 (.f64 (fma.f64 x y z) (fma.f64 (.f64 x y) (-.f64 (.f64 x y) z) (.f64 z z))) (-.f64 (.f64 (.f64 x y) (.f64 x (.f64 x (.f64 y y)))) (.f64 z (.f64 z z))))) #s(literal -1 binary64)) (/.f64 #s(literal 1 binary64) (fma.f64 x (.f64 (.f64 x (.f64 y y)) (.f64 x (.f64 x (.f64 y y)))) (.f64 (.f64 z z) (fma.f64 y (.f64 x (.f64 x y)) (*.f64 z z))))))
(.f64 (pow.f64 (/.f64 (-.f64 (.f64 x y) z) (.f64 (.f64 (fma.f64 x y z) (-.f64 (.f64 x y) z)) (fma.f64 y (.f64 x (.f64 x y)) (.f64 z z)))) #s(literal -1 binary64)) (/.f64 #s(literal 1 binary64) (fma.f64 y (.f64 x (.f64 x y)) (*.f64 z z))))
(.f64 (pow.f64 (/.f64 (fma.f64 (.f64 x y) (-.f64 (.f64 x y) z) (.f64 z z)) (fma.f64 (.f64 (.f64 x y) (.f64 x (.f64 x (.f64 y y)))) (.f64 (.f64 (.f64 x y) (.f64 x (.f64 x (.f64 y y)))) (.f64 (.f64 x y) (.f64 x (.f64 x (.f64 y y))))) (.f64 (.f64 z (.f64 z z)) (.f64 (.f64 z (.f64 z z)) (.f64 z (.f64 z z)))))) #s(literal -1 binary64)) (/.f64 #s(literal 1 binary64) (fma.f64 (.f64 (.f64 x y) (.f64 x (.f64 x (.f64 y y)))) (.f64 (.f64 x y) (.f64 x (.f64 x (.f64 y y)))) (.f64 (.f64 z (.f64 z z)) (-.f64 (.f64 z (.f64 z z)) (.f64 (.f64 x y) (.f64 x (.f64 x (.f64 y y)))))))))
(.f64 (pow.f64 (/.f64 (fma.f64 (.f64 x y) (-.f64 (.f64 x y) z) (.f64 z z)) (.f64 (.f64 (fma.f64 x y z) (fma.f64 (.f64 x y) (-.f64 (.f64 x y) z) (.f64 z z))) (-.f64 (.f64 (.f64 x y) (.f64 x (.f64 x (.f64 y y)))) (.f64 z (.f64 z z))))) #s(literal -1 binary64)) (/.f64 #s(literal 1 binary64) (-.f64 (.f64 (.f64 x y) (.f64 x (.f64 x (.f64 y y)))) (.f64 z (*.f64 z z)))))
(*.f64 (pow.f64 (/.f64 #s(literal 1 binary64) (fma.f64 x y z)) #s(literal -1/2 binary64)) (pow.f64 (/.f64 #s(literal 1 binary64) (fma.f64 x y z)) #s(literal -1/2 binary64)))

simplify591.0ms (9.8%)

Memory

-5.0MiB live, 925.7MiB allocated

Algorithm

1×	egg-herbie

Rules

29 446×	`lower-fma.f64`
29 446×	`lower-fma.f32`
3 824×	`lower-+.f64`
3 824×	`lower-+.f32`
2 912×	`lower-*.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	32	190
1	106	190
2	287	190
3	739	190
4	2060	190
5	3234	190
6	4834	190
7	5836	190
8	6509	190
9	6762	190
0	8782	163

Stop Event

1×	iter limit
1×	node limit

Counts

48 → 44

Calls

Call 1

Inputs
(* 1/2 x)
(* 1/2 x)
(* 1/2 x)
(* 1/2 x)
(* 1/2 x)
(* 1/2 x)
(* 1/2 x)
(* 1/2 x)
(* 1/2 x)
(* 1/2 x)
(* 1/2 x)
(* 1/2 x)
z
(+ z (* x y))
(+ z (* x y))
(+ z (* x y))
(* x y)
(* y (+ x (/ z y)))
(* y (+ x (/ z y)))
(* y (+ x (/ z y)))
(* x y)
(* -1 (* y (+ (* -1 x) (* -1 (/ z y)))))
(* -1 (* y (+ (* -1 x) (* -1 (/ z y)))))
(* -1 (* y (+ (* -1 x) (* -1 (/ z y)))))
z
(+ z (* x y))
(+ z (* x y))
(+ z (* x y))
(* x y)
(* x (+ y (/ z x)))
(* x (+ y (/ z x)))
(* x (+ y (/ z x)))
(* x y)
(* -1 (* x (+ (* -1 y) (* -1 (/ z x)))))
(* -1 (* x (+ (* -1 y) (* -1 (/ z x)))))
(* -1 (* x (+ (* -1 y) (* -1 (/ z x)))))
(* x y)
(+ z (* x y))
(+ z (* x y))
(+ z (* x y))
z
(* z (+ 1 (/ (* x y) z)))
(* z (+ 1 (/ (* x y) z)))
(* z (+ 1 (/ (* x y) z)))
z
(* -1 (* z (- (* -1 (/ (* x y) z)) 1)))
(* -1 (* z (- (* -1 (/ (* x y) z)) 1)))
(* -1 (* z (- (* -1 (/ (* x y) z)) 1)))

Outputs
(* 1/2 x)
(*.f64 #s(literal 1/2 binary64) x)
(* 1/2 x)
(*.f64 #s(literal 1/2 binary64) x)
(* 1/2 x)
(*.f64 #s(literal 1/2 binary64) x)
(* 1/2 x)
(*.f64 #s(literal 1/2 binary64) x)
(* 1/2 x)
(*.f64 #s(literal 1/2 binary64) x)
(* 1/2 x)
(*.f64 #s(literal 1/2 binary64) x)
(* 1/2 x)
(*.f64 #s(literal 1/2 binary64) x)
(* 1/2 x)
(*.f64 #s(literal 1/2 binary64) x)
(* 1/2 x)
(*.f64 #s(literal 1/2 binary64) x)
(* 1/2 x)
(*.f64 #s(literal 1/2 binary64) x)
(* 1/2 x)
(*.f64 #s(literal 1/2 binary64) x)
(* 1/2 x)
(*.f64 #s(literal 1/2 binary64) x)
z
(+ z (* x y))
(fma.f64 x y z)
(+ z (* x y))
(fma.f64 x y z)
(+ z (* x y))
(fma.f64 x y z)
(* x y)
(*.f64 x y)
(* y (+ x (/ z y)))
(fma.f64 x y z)
(* y (+ x (/ z y)))
(fma.f64 x y z)
(* y (+ x (/ z y)))
(fma.f64 x y z)
(* x y)
(*.f64 x y)
(* -1 (* y (+ (* -1 x) (* -1 (/ z y)))))
(fma.f64 x y z)
(* -1 (* y (+ (* -1 x) (* -1 (/ z y)))))
(fma.f64 x y z)
(* -1 (* y (+ (* -1 x) (* -1 (/ z y)))))
(fma.f64 x y z)
z
(+ z (* x y))
(fma.f64 x y z)
(+ z (* x y))
(fma.f64 x y z)
(+ z (* x y))
(fma.f64 x y z)
(* x y)
(*.f64 x y)
(* x (+ y (/ z x)))
(fma.f64 x y z)
(* x (+ y (/ z x)))
(fma.f64 x y z)
(* x (+ y (/ z x)))
(fma.f64 x y z)
(* x y)
(*.f64 x y)
(* -1 (* x (+ (* -1 y) (* -1 (/ z x)))))
(fma.f64 x y z)
(* -1 (* x (+ (* -1 y) (* -1 (/ z x)))))
(fma.f64 x y z)
(* -1 (* x (+ (* -1 y) (* -1 (/ z x)))))
(fma.f64 x y z)
(* x y)
(*.f64 x y)
(+ z (* x y))
(fma.f64 x y z)
(+ z (* x y))
(fma.f64 x y z)
(+ z (* x y))
(fma.f64 x y z)
z
(* z (+ 1 (/ (* x y) z)))
(fma.f64 x y z)
(* z (+ 1 (/ (* x y) z)))
(fma.f64 x y z)
(* z (+ 1 (/ (* x y) z)))
(fma.f64 x y z)
z
(* -1 (* z (- (* -1 (/ (* x y) z)) 1)))
(fma.f64 x y z)
(* -1 (* z (- (* -1 (/ (* x y) z)) 1)))
(fma.f64 x y z)
(* -1 (* z (- (* -1 (/ (* x y) z)) 1)))
(fma.f64 x y z)

eval30.0ms (0.5%)

Memory: 2.8MiB live, 81.9MiB allocated
Compiler: Compiled 9 772 to 503 computations (94.9% saved)

prune35.0ms (0.6%)

Memory

-6.2MiB live, 112.4MiB allocated

Pruning

6 alts after pruning (0 fresh and 6 done)

	Pruned	Kept	Total
New	257	0	257
Fresh	0	0	0
Picked	0	2	2
Done	0	4	4
Total	257	6	263

Accuracy

100.0%

Counts

263 → 6

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	100.0%	(fma.f64 (+.f64 y #s(literal 1/2 binary64)) x z)
✓	78.0%	(fma.f64 y x z)
✓	61.3%	(fma.f64 x #s(literal 1/2 binary64) z)
✓	61.4%	(*.f64 x (+.f64 #s(literal 1/2 binary64) y))
✓	39.8%	(*.f64 x y)
✓	23.1%	(*.f64 x #s(literal 1/2 binary64))

Compiler

Compiled 85 to 48 computations (43.5% saved)

regimes17.0ms (0.3%)

Memory

6.4MiB live, 45.8MiB allocated

Counts

8 → 1

Calls

Call 1

Inputs
(*.f64 x #s(literal 1/2 binary64))
(*.f64 x y)
(fma.f64 x #s(literal 1/2 binary64) z)
(fma.f64 y x z)
(*.f64 x (+.f64 #s(literal 1/2 binary64) y))
(+.f64 (*.f64 x y) z)
(fma.f64 (+.f64 y #s(literal 1/2 binary64)) x z)
(+.f64 (+.f64 (/.f64 x #s(literal 2 binary64)) (*.f64 y x)) z)

Outputs
(fma.f64 (+.f64 y #s(literal 1/2 binary64)) x z)

Calls

5 calls:

4.0ms	(+.f64 (/.f64 x #s(literal 2 binary64)) (*.f64 y x))
3.0ms	z
3.0ms	x
3.0ms	(+.f64 (+.f64 (/.f64 x #s(literal 2 binary64)) (*.f64 y x)) z)
3.0ms	y

Results

Accuracy	Segments	Branch
100.0%	1	`x`
100.0%	1	`y`
100.0%	1	`z`
100.0%	1	`(+.f64 (+.f64 (/.f64 x #s(literal 2 binary64)) (*.f64 y x)) z)`
100.0%	1	`(+.f64 (/.f64 x #s(literal 2 binary64)) (*.f64 y x))`

Compiler

Compiled 34 to 24 computations (29.4% saved)

regimes15.0ms (0.2%)

Memory

2.2MiB live, 40.9MiB allocated

Counts

6 → 3

Calls

Call 1

Inputs
(*.f64 x #s(literal 1/2 binary64))
(*.f64 x y)
(fma.f64 x #s(literal 1/2 binary64) z)
(fma.f64 y x z)
(*.f64 x (+.f64 #s(literal 1/2 binary64) y))
(+.f64 (*.f64 x y) z)

Outputs
(fma.f64 y x z)
(fma.f64 x #s(literal 1/2 binary64) z)
(fma.f64 y x z)

Calls

5 calls:

4.0ms	(+.f64 (/.f64 x #s(literal 2 binary64)) (*.f64 y x))
3.0ms	x
3.0ms	z
3.0ms	(+.f64 (+.f64 (/.f64 x #s(literal 2 binary64)) (*.f64 y x)) z)
3.0ms	y

Results

Accuracy	Segments	Branch
91.2%	3	`x`
98.0%	3	`y`
88.2%	3	`z`
81.8%	3	`(+.f64 (+.f64 (/.f64 x #s(literal 2 binary64)) (*.f64 y x)) z)`
89.1%	3	`(+.f64 (/.f64 x #s(literal 2 binary64)) (*.f64 y x))`

Compiler

Compiled 34 to 24 computations (29.4% saved)

regimes10.0ms (0.2%)

Memory

-17.3MiB live, 21.3MiB allocated

Counts

3 → 3

Calls

Call 1

Inputs
(*.f64 x #s(literal 1/2 binary64))
(*.f64 x y)
(fma.f64 x #s(literal 1/2 binary64) z)

Outputs
(*.f64 x y)
(fma.f64 x #s(literal 1/2 binary64) z)
(*.f64 x y)

Calls

4 calls:

3.0ms	y
2.0ms	x
2.0ms	z
2.0ms	(+.f64 (/.f64 x #s(literal 2 binary64)) (*.f64 y x))

Results

Accuracy	Segments	Branch
66.5%	3	`z`
75.9%	3	`(+.f64 (/.f64 x #s(literal 2 binary64)) (*.f64 y x))`
67.4%	4	`x`
82.9%	3	`y`

Compiler

Compiled 22 to 16 computations (27.3% saved)

regimes12.0ms (0.2%)

Memory

-28.8MiB live, 22.0MiB allocated

Counts

2 → 3

Calls

Call 1

Inputs
(*.f64 x #s(literal 1/2 binary64))
(*.f64 x y)

Outputs
(*.f64 x y)
(*.f64 x #s(literal 1/2 binary64))
(*.f64 x y)

Calls

5 calls:

2.0ms	z
2.0ms	x
2.0ms	(+.f64 (+.f64 (/.f64 x #s(literal 2 binary64)) (*.f64 y x)) z)
2.0ms	(+.f64 (/.f64 x #s(literal 2 binary64)) (*.f64 y x))
2.0ms	y

Results

Accuracy	Segments	Branch
41.7%	2	`x`
39.8%	1	`z`
43.7%	3	`(+.f64 (/.f64 x #s(literal 2 binary64)) (*.f64 y x))`
43.6%	3	`(+.f64 (+.f64 (/.f64 x #s(literal 2 binary64)) (*.f64 y x)) z)`
59.6%	3	`y`

Compiler

Compiled 34 to 24 computations (29.4% saved)

regimes7.0ms (0.1%)

Memory

15.7MiB live, 15.7MiB allocated

Accuracy

Total -0.0b remaining (-0%)

Threshold costs -0b (-0%)

Counts

1 → 1

Calls

Call 1

Inputs
(*.f64 x #s(literal 1/2 binary64))

Outputs
(*.f64 x #s(literal 1/2 binary64))

Calls

5 calls:

1.0ms	(+.f64 (/.f64 x #s(literal 2 binary64)) (*.f64 y x))
1.0ms	z
1.0ms	(+.f64 (+.f64 (/.f64 x #s(literal 2 binary64)) (*.f64 y x)) z)
1.0ms	y
1.0ms	x

Results

Accuracy	Segments	Branch
23.1%	1	`z`
23.1%	1	`x`
23.1%	1	`(+.f64 (+.f64 (/.f64 x #s(literal 2 binary64)) (*.f64 y x)) z)`
23.1%	1	`(+.f64 (/.f64 x #s(literal 2 binary64)) (*.f64 y x))`
23.1%	1	`y`

Compiler

Compiled 34 to 24 computations (29.4% saved)

bsearch121.0ms (2%)

Memory

-4.3MiB live, 34.8MiB allocated

Algorithm

2×	binary-search

Stop Event

1×	narrow-enough
1×	narrow-enough

Steps

Time	Left	Right
105.0ms	0.06718860101336342	3.520736547582319
13.0ms	-3660577737647.657	-0.01367935842192179

Samples

109.0ms

272×

valid

Compiler

Compiled 287 to 201 computations (30% saved)

Precisions

Click to see histograms. Total time spent on operations: 103.0ms

ival-mult: 98.0ms (95.5% of total)

ival-div: 2.0ms (1.9% of total)

ival-add: 2.0ms (1.9% of total)

ival-true: 0.0ms (0% of total)

exact: 0.0ms (0% of total)

ival-assert: 0.0ms (0% of total)

bsearch21.0ms (0.3%)

Memory

28.1MiB live, 28.1MiB allocated

Algorithm

2×	binary-search

Stop Event

1×	narrow-enough
1×	narrow-enough

Steps

Time	Left	Right
7.0ms	0.06718860101336342	3.520736547582319
12.0ms	-3660577737647.657	-0.01367935842192179

Samples

10.0ms

224×

valid

Compiler

Compiled 270 to 201 computations (25.6% saved)

Precisions

Click to see histograms. Total time spent on operations: 5.0ms

ival-div: 2.0ms (38.5% of total)

ival-add: 2.0ms (38.5% of total)

ival-mult: 1.0ms (19.2% of total)

ival-true: 0.0ms (0% of total)

exact: 0.0ms (0% of total)

ival-assert: 0.0ms (0% of total)

bsearch4.0ms (0.1%)

Memory

-34.6MiB live, 3.0MiB allocated

Algorithm

2×	binary-search

Stop Event

1×	narrow-enough
1×	narrow-enough

Steps

Time	Left	Right
1.0ms	0.06718860101336342	3.520736547582319
3.0ms	-3660577737647.657	-0.01367935842192179

Compiler

Compiled 253 to 201 computations (20.6% saved)

simplify7.0ms (0.1%)

Memory

8.8MiB live, 8.8MiB allocated

Algorithm

1×	egg-herbie

Rules

4×	`*-commutative_binary64`
2×	`+-commutative_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	23	64
1	26	64

Stop Event

1×

saturated

Calls

Call 1

Inputs
(fma.f64 (+.f64 y #s(literal 1/2 binary64)) x z)
(if (<=.f64 y #s(literal -1/2 binary64)) (fma.f64 y x z) (if (<=.f64 y #s(literal 1/2 binary64)) (fma.f64 x #s(literal 1/2 binary64) z) (fma.f64 y x z)))
(if (<=.f64 y #s(literal -7200000000 binary64)) (.f64 x y) (if (<=.f64 y #s(literal 7/2 binary64)) (fma.f64 x #s(literal 1/2 binary64) z) (.f64 x y)))
(if (<=.f64 y #s(literal -1/2 binary64)) (.f64 x y) (if (<=.f64 y #s(literal 1/2 binary64)) (.f64 x #s(literal 1/2 binary64)) (*.f64 x y)))
(*.f64 x #s(literal 1/2 binary64))

Outputs
(fma.f64 (+.f64 y #s(literal 1/2 binary64)) x z)
(if (<=.f64 y #s(literal -1/2 binary64)) (fma.f64 y x z) (if (<=.f64 y #s(literal 1/2 binary64)) (fma.f64 x #s(literal 1/2 binary64) z) (fma.f64 y x z)))
(if (<=.f64 y #s(literal -7200000000 binary64)) (.f64 x y) (if (<=.f64 y #s(literal 7/2 binary64)) (fma.f64 x #s(literal 1/2 binary64) z) (.f64 x y)))
(if (<=.f64 y #s(literal -7200000000 binary64)) (.f64 y x) (if (<=.f64 y #s(literal 7/2 binary64)) (fma.f64 x #s(literal 1/2 binary64) z) (.f64 y x)))
(if (<=.f64 y #s(literal -1/2 binary64)) (.f64 x y) (if (<=.f64 y #s(literal 1/2 binary64)) (.f64 x #s(literal 1/2 binary64)) (*.f64 x y)))
(if (<=.f64 y #s(literal -1/2 binary64)) (.f64 y x) (if (<=.f64 y #s(literal 1/2 binary64)) (.f64 #s(literal 1/2 binary64) x) (*.f64 y x)))
(*.f64 x #s(literal 1/2 binary64))
(*.f64 #s(literal 1/2 binary64) x)

soundness931.0ms (15.5%)

Memory

10.5MiB live, 569.8MiB allocated

Rules

8 308×	`lower-fma.f32`
8 304×	`lower-fma.f64`
8 198×	`lower-fma.f64`
8 198×	`lower-fma.f32`
7 074×	`lower-fma.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	11	29
0	20	29
1	84	29
2	630	29
3	7950	29
0	8328	28
0	85	720
1	290	720
2	795	720
3	2300	720
4	4011	720
5	6468	720
0	8258	647
0	8	22
0	12	22
1	52	18
2	452	18
3	6077	18
0	8040	17
0	57	440
1	174	440
2	488	440
3	1310	440
4	3612	440
5	6659	440
0	8189	412

Stop Event

1×	done
1×	iter limit
1×	node limit
1×	iter limit
1×	node limit
1×	iter limit
1×	iter limit
1×	node limit
1×	iter limit
1×	node limit
1×	iter limit

Compiler

Compiled 145 to 78 computations (46.2% saved)

preprocess35.0ms (0.6%)

Memory: 9.4MiB live, 82.8MiB allocated
Compiler: Compiled 158 to 62 computations (60.8% saved)

end0.0ms (0%)

Memory: 0.0MiB live, 0.0MiB allocated

analyze0.0ms (0%)

sample1.4s (23.6%)

preprocess70.0ms (1.2%)

explain94.0ms (1.6%)

eval0.0ms (0%)

prune1.0ms (0%)

simplify5.0ms (0.1%)

localize24.0ms (0.4%)

series6.0ms (0.1%)

rewrite327.0ms (5.4%)

simplify209.0ms (3.5%)

eval38.0ms (0.6%)

prune37.0ms (0.6%)

simplify6.0ms (0.1%)

localize41.0ms (0.7%)

series5.0ms (0.1%)

rewrite547.0ms (9.1%)

simplify328.0ms (5.5%)

eval157.0ms (2.6%)

prune209.0ms (3.5%)

simplify5.0ms (0.1%)

localize18.0ms (0.3%)

series1.0ms (0%)

rewrite634.0ms (10.5%)

simplify591.0ms (9.8%)

eval30.0ms (0.5%)

prune35.0ms (0.6%)

regimes17.0ms (0.3%)

regimes15.0ms (0.2%)

regimes10.0ms (0.2%)

regimes12.0ms (0.2%)

regimes7.0ms (0.1%)

bsearch121.0ms (2%)

bsearch21.0ms (0.3%)

bsearch4.0ms (0.1%)

simplify7.0ms (0.1%)

soundness931.0ms (15.5%)

preprocess35.0ms (0.6%)

end0.0ms (0%)

Profiling